כמה מרובע יתר על העיגול רביע—How much is a square larger than a circle; a fourth

OVERVIEW If a circle is inscribed within a square, the area of the square will be a fourth larger than the area of the circle.¹

This ratio is cited in a ברייתא in מסכת מדות and so too in מסכת עירובין.

SUMMARY This ratio is cited elsewhere in the גמרא.

THINKING IT OVER There is a משנה in מס' אהלות פי"ב מ"ו which states that שהמרובע יותר על העגול רביע. Why did not תוספות cite this משנה, rather than citing a ברייתא and a גמרא?!

footnotes: ¹ This would mean if the area of a square (4x4) is sixteen, the area of a circle (with a diameter of 4) will be twelve; a fourth less than the square. This holds true if we assume (as the גמרא does) the value for pi to be 3. [𝐴=𝜋𝑟2] Pi is the ratio of the circumference of a circle to its diameter. According to pi = 3 if the diameter of a circle is one, the circumference is three. ² יד,ב וש"נ. See ‘Thinking it over’.

הכי גרס רבינו תם פש להו תרי תילתא אמתא—This is how Rabainu Tahm reads the text; ‘there still remains two-thirds of an Ahmoh’

OVERVIEW עולא maintains that a tree is יונק from an circular area with a radius of 16 אמות around the tree. This is an area of 768 square אמות.¹ From the משנה on כו,ב regarding three trees in a בית סאה (which is 2500 square אמות) it turns out that each tree is יונק an area of 833 and 1/3 square אמות. We have here a discrepancy of 65 and 1/3 square אמות, which עולא is less than the משנה. In order to make the measurement of עולא (nearly) equal to the משנה, we will need to increase the radius to somewhat more than 16. The גירסא in our גמרא is that we are missing one-half אמה (meaning that the radius should be 16.5 אמות), while according to the ר"ת it should be increased 2/3 of an אמה to 16 and 2/3).²

פירוש כשתקיף אילן דעולא רצועה רחבה שני שלישי אמה³ – The explanation of פש להו תרי תילתא אמתא (we are missing 2/3 of an אמה) is that when you will surround the tree of עולא (which has a radius of 16 אמה) with a strip of land which is 2/3 of an אמה wide, meaning that the radius will now be 16 and 2/3 אמה, this new area of יניקה – יהא גדול כאילן המשנה שהיה יותר ס"ה אמות ושליש ברוחב אמה⁴ – Will be as large as the tree of the משנה whose area was larger by 65 and 1/3 אמה with a width of an אמה (meaning 65 and 1/3 sq. אמות) –**** תוספות will now show how adding the additional 2/3 אמות, will make sעולא' tree יונק from the same area as the משנה tree: שהרי אם תקיף ל"ב על ל"ב מרובעים⁵ יצטרך קכ"ח⁶ ולד' קרנות ח' שלישים⁷ – For if you will surround a square of 32 by 32 with a strip of 2/3 אמה width, it will require a strip of 128 אמה long and for the four corners an additional 8/3 אמה – הרי ק"ל ושני שלישים⁸ אורך על שני שלישים רוחב – So now we have a strip of 130 and 2/3 אמות long by 2/3 אמה wide; this is the extra area added on by adding 2/3 אמה around the entire square. However, this is by a square, but we are dealing with a circle, therefore – תחסר הרביע⁹ שהעיגול פחות ישאר צ"ח – Diminish this amount by a fourth, which is the amount the area of a circle is less than a square (who share the same diameter) there will remain a strip of 98 by 2/3 אמה; we now have the area we have added to עולא, by adding the strip of 2/3 אמה, namely 98 x2/3 אמה. This will equal the 65 1/3 אמה which the משנה was greater than עולא, as תוספות will now show – וכן ס"ה אמה ושליש תחתוך לג' חלקים לאורך תהיה רצועה אחת של קצ"ו¹⁰ ברוחב שליש – And similarly, the 65 and 1/3 אמה (which is the amount the area of the משנה was greater than the original area of עולא), take this strip and cut it in the length into three equal parts and put them next to each other in length, you will have one strip of 196 אמה long by 1/3 אמה wide – תחתוך לשנים ותשים זה בצד זה תהיה רצועה ארכה צ"ח על רוחב שני שלישי¹¹ אמה¹² – Cut this long strip of 196 אמה into two equal parts (each one 98 אמה) there will be a strip of 98 אמה long by a width of 2/3 אמה. תוספות offers an alternate method to reconcile the אילן דעולא with the אילן דמשנה: עוד מצא רבינו יצחק בספר¹³ אחר מפורש בגמרת הספר להקיף בחוטים¹⁴ אילן דעולא – Additionally, the ר"י found in another ספר, expressed in the margin of the ספר, to surround, with threads, the outside circumference of the עולא tree – שהוא ל"ב על ל"ב עד שיהא¹⁵ שני שלישי אמה סביב¹⁶ – Which has a diameter of 32 by 32, there should be sufficient threads until the [width of these threads] will be 2/3 of an אמה wide around the entire circumference – תחתוך החוטין ותפשטם יהיה העליון ארכו ק' שהוא מקיף ל"ג ושליש¹⁷ – Cut the threads and stretch them out in a straight line, the upper (outside) thread will be 100 אמה long since it encircles a diameter of 33 and 1/3 – וכל שיש ברחבו טפח יש בהיקפו ג'¹⁸ – And the rule is that if the diameter is a טפח, the circumference is three טפחים – והתחתון צ"ו שהוא מקיף ל"ב¹⁹ הרי²⁰ התחתון פחות מן העליון מכל צד ב' אמות²¹ – And the lower (inner) thread is 96 אמות long, since it surrounds the actual diameter of 32, so the [length] of the inner thread is less than the outer thread 2 אמות on each side – ותחתוך העודף מצד אחד ותמלא צד אחד²² האורך לצד הקצר²³ תהיה רצועה צ"ח²⁴ – And cut off the extra threads that protrude from one side of the outer threads, and fill in the other side, the long next to the short so you will have a strip of 98 אמה by 2/3 אמה וכן הוא ס"ה ושליש – Which is the same as 65 and 1/3 by one אמה – Another way of equalizing אילן דעולא with the אילן דמשנה: דרך אחרת ל"ג ושליש על ל"ג ושליש²⁵ מרובעים עולה – Another way; 33 and 1/3 by 33 and 1/3 squared, equals – אלף ומאה וי"א אמות ושליש של שליש שהיא תשיעית אמה²⁶ – Eleven hundred eleven sq. אמות plus a third of a third which is a ninth of an אמה – תחסר הרביעית ישאר תתל"ג ושליש²⁷ הרי אילן המשנה ל"ג ושליש על ל"ג ושליש – Subtract a fourth (since we are discussing a circle) the remainder is 833 and 1/3 אמה**, which is the** equivalent of the משנה tree, which is 33 and 1/3 by 33 and 1/3. Another calculation: (הג"ה. או כעין זה שליש סאה²⁸ הוי י"ו וב' שלישים על חמשים²⁹ – )A gloss: Or something like this, a third of a בית סאה is 16 and 2/3 by 50 – חתוך באמצע ושים זה על זה יהיה עשרים וחמש על שלשים ושלש ושליש³⁰) – Cut the fifty אמה length in the middle and place one next to the other you will have 25 by 33 and 1/3(. Another calculation: דרך אחרת בית סאה היא מאה על כ"ה³¹ תקח השליש לאילן אחד יהיה ל"ג ושליש על כ"ה – Another way; a בית סאה is 100 by 25, take one third for one tree, his area will be 33 and 1/3 by 25 in a rectangle – והם ל"ג ושליש על ל"ג ושליש עגולים – Which is the equivalent of a circle with a diameter of 33 and 1/3; תוספות shows how – שהרי מוסיף הרביע מלבר שהיא שליש מלגיו³² – Since we add to the area of a circle a fourth from the outside which is a third from the inside – דהיינו ח' אמה ושליש³³ באורך ל"ג ושליש יהיו ל"ג ושליש על ל"ג ושליש מרובעים – Which is 8 and 1/3, to a length of 33 and 1/3, there will then be 33 and 1/3 squared – (ולספרים דגרסינן פש להו פלגא דאמתא³⁴) – ועשה אותו עגול שיחסר הרביע שהוספת³⁵ ויהיה עגול ל"ג ושליש על ל"ג ושליש-– And make this round, meaning subtract the fourth which we added, so it will be a circle of 33 and 1/3 by 33 and 1/3. תוספות concluded explaining the גמרא according to his גירסא of תרי תלתא אמתא, now תוספות will explain the גמרא according to the גירסא of פלגא דאמתא: ולספרים דגרסי פש ליה פלגא דאמתא יש לפרש דחשיב עולא י"ו לכל צד לבד מקום האילן – And according to the text which are גורס, ‘there is missing half an אמה’, we can explain that when עולא counts the sixteen אמות in all directions, that is excluding the place the tree occupies – ומקום אילן שליש על שליש נמצא אילן דעולא ל"ב ושליש על ל"ב ושליש³⁶ – And the tree occupies a diameter of a third אמה, it turns out that the diameter of אילן דעולא is 32 and 1/3 – כשתקיף מכל צד פלגא דאמתא יהיה ל"ג ושליש על ל"ג ושליש³⁷ – So when you will add the extra half אמה (פלגא דאמתא) around the entire circumference you will have a diameter of 33 and 1/3; which is the same as the אילן דמשנה. Another explanation and גירסא in our גמרא: ורבינו משולם מפרש דעולא לא חשיב מקום האילן³⁸ ומקום האילן הוי אמה על אמה – And רבינו משולם explains that עולא does not count the place of the tree, however the tree occupies an אמה in diameter (not a third of an אמה as in the previous explanation) – נמצא דהוי אילן דעולא ל"ג על ל"ג ואם היו מרובעים היה עולה אלף ופ"ט – It turns out that אילן דעולא has a diameter of 33, and if it were squared it would add up to 1089 sq. אמות – תחסר הרביע ישאר תתי"ו ושלשה רבעי אמה³⁹ – Subtract a quarter for the area of a circle with a diameter of 33, there will remain an area of 816 ¾ אמה. ולא גרסינן (והוו) [פשו] להו ז' מאה ושתין ותמניא – And we are not גורס, ‘there remains 768’ sq. אמות, rather there remains 816 ¾ אמות – נמצא דאילן המשנה יתר על של עולא י"ו אמה ושליש ורביע⁴⁰ – It turns out that the אילן המשנה is larger than אילן דעולא by 16 7/12 אמה – ופלגא דאמתא קאי אבית סאה שהיא חמשים על חמשים – And when the גמרא states פש ליה פלגא דאמתא, it is referring to the בית סאה which is 50 x 50 – כשתסיר פלגא דאמתא לאורך וכן לרוחב יעלה החסרון חמשים אמה חסר רביע⁴¹ – That when you will remove half an אמה in the length and similarly half an אמה in the width, the part subtracted will be 49 ¾ אמה – דהיינו לג' אילנות ולאילן אחד יעלה י"ו אמה ושליש ורביע⁴² וישאר⁴³ כאילן דעולא: This amount of 49 ¾ is for three trees but for one tree for one tree it will equal 16 7/12, so the remainder will be the same as אילן דעולא.

SUMMARY There are various ways of reconciling the אילן דעולא with אילן דמשנה.

THINKING IT OVER Why was it necessary for תוספות to cite more than one example how to reconcile אילן דעולא with אילן דמשנה?

footnotes: ¹ The גמרא reaches this conclusion by first squaring the area (which is 32 x 32 אמות [twice the radius of 16[) which is 1024 square אמות. We then reduce the area of a circle from the area of a square by ¼ (which is 256); subtract that from 1024 it equals 768. Using the equation of 𝐴=𝜋𝑟2 (where 𝜋=3 as the גמרא assumes), we achieve the same result; 3 x 16 x 16 = 768. [A is the area of the circle; 𝜋 is the symbol for pi which is the ratio of the circumference of a circle to its diameter. This is not an exact number; the גמרא assumes it to be 3, and r refers to the radius of the circle.] ² Using the same formula as in footnote # 1 if r = 16.5 (as in our גירסא) the area will be 816.75 (still a difference of 16.58 sq. אמות approximately, from the משנה); if, however, r = 16.66... (as the ר"ת would have it) the area would be 833.33; virtually the same as the משנה. This is why the ר"ת prefers his גירסא. However, it seems that they did not use this formula (in footnote # 1) in those days, therefore it was necessary for תוספות to use other methods to achieve his goal of finding the right amount that the radius needs to be increased, in order to match עולא with the משנה. ³ This means literally that if you will add a strip of land 2/3 of an אמה outside the circumference of the circle which has a radius of sixteen אמות from the tree (making the new radius 16 2/3 אמות). ⁴ See ‘Overview’ and in the גמרא. ⁵ We begin by assuming that the sixteen אמה radius (which is 32 אמה diameter) is a square of 32 אמות (on each side) instead of a circle with a 32 אמה diameter. The way the גמרא calculates the area of a circle is by first assuming a square with the same size as the diameter of the circle, then after calculating the area of the square, they would reduce it by ¼ and that would give the area of a circle, so that a circle inscribed in a square 2x2 which has an area of 4 (2x2 =4), the circle (which has a radius of 1), will have an area of 3, a fourth less than the square. ⁶ The perimeter of a 32x32 square is 128 (32x4=128). However, we need to add the strip to each of the four corners; each corner will require a strip of 2/3x2/3 אמה to complete adding 2/3 of an אמה to the entire square. ⁷ 8/3 = 2 and 2/3. ⁸ 128 + 8/3 or 128 + 2 and 2/3 = 130 and 2/3. ⁹ 130.66.. x .75 = 97.99995 or actually 98. We are using only whole numbers. Alternately 130.66/4= 32.665; 130.66-32.665=98. ¹⁰ 65 1/3 x 3 = 196 [65x3=195, and 1/3x 3=1; in total 196]. ¹¹ The long strip was 1/3 אמה wide when they are joined in the width it is 2/3 אמה wide. ¹² This area 98x2/3 is exactly the same as the area of עולא if we add a strip of 2/3 אמה. ¹³ The הגהות הב"ח amends this to read בספר אחד מפורש בגליון הספר (instead of בספר אחר מפורש בגמרת הספר). ¹⁴ The advantage of this explanation over the previous one is that practically one cannot take a strip which is a rectangle 2/3 אמה wide and place it around a circle since the circle is round and a strip is straight; however, with thin threads one can imagine circling the circle with the threads. ¹⁵ The הגהות הב"ח amends this to read שיהא רוחב החוט(ין) שני (instead of שיהא שני). ¹⁶ The עולא tree has a diameter of 32 אמה. Mark off the circumference of this diameter, and start encircling this circumference (beginning immediately next to the edge of the circumference) with many threads next to each other, until the width from the most outside thread to the edge of the circumference is 2/3 אמה. ¹⁷ The outer thread was 2/3 אמה beyond the circumference (see footnote # 16), this addition is on both (all) sides of the circle; the new diameter (the diameter of this thread is) is an additional (2 x 2/3 or) 1 and 1/3 אמה, making the total diameter 33 and 1/3. [32 + 1 and 1/3 = 33 1/3]. ¹⁸ This is the number used for pi in the גמרא in the formula C = pi x diameter. Therefore since the diameter is 33 and 1/3, so 3 x 33 and 1/3 = 100. [the current number for pi is 3.1415…] ¹⁹ 32 x 3 = 96. ²⁰ The הגהות הב"ח amends this to read הרי אורך התחתון (instead of הרי התחתון). ²¹ It is 4 אמות less (100-96=4). If we line up the threads by their center, we can view the closest (shortest) thread as 2 אמות less on each side than the outside (longest) thread. ²² The רש"ש amends this to read אחר (instead of אחד). ²³ Let us assume that there are five threads ranging in length (from the inside out) at 96,97,98,99,100. When they are lying straight the 100 thread is two אמות longer on each end than the 96 thread and one אמה longer than the 98 thread, (1/2 from the 99 thread and 1½ from the 97 thread). When we cut the five threads at one end, there are two אמות from the 100 thread and 1 אמה from the 98 thread (1/2 and 1 ½ from the 97 and 99 threads respectively). We then take these threads flip them and place them on the other side The longer cut piece to the shorter thread, so that the 2 אמות from the 100 thread goes on the 96 thread making it 98 and the one אמה from the 98 thread (which now became a 97 thread) goes on the original 98 thread and it remains 98, etc.; in short all 5 threads become 98 אמה threads. ²⁴ 98 by 2/3 = 65 1/3 x 1 אמה. [ 98x2=196; 196/3 = 65 and 1/3] ²⁵ We are aiding 2/3 אמה to the length and width of the original 32x32. This comes to 33 1/3. ²⁶ 33 1/3 x 33 1/3 = 100/3 x 100/3 = 10,000/3 = 1111 1/9. ²⁷ 1111.11x.75=833.33. ²⁸ In the משנה there are three trees in a בית סאה, which is 50x50 אמה. ²⁹ 50/3= 16 2/3. ³⁰ 25x33.333=833.325. ³¹ A בית סאה is 2500 sq. אמה which is 50 by 50, or 100 by 25. ³² A circle inscribed in a square that has an area of four, will have an area of three. The area of the square is ‘one’ more than the circle. This ‘one’ can be considered a third of the area of the circle (מלגיו), or it can be considered a fourth of the entire area of the square (מלבר). We reduce the area of a square by a fourth to get the area of a inscribed circle and we increase the area of the inscribed circle by one third to get the area of the square ³³ A third מלגיו of 25 is 8 1/3. ³⁴ The רש"ל deletes the entire parenthesis. ³⁵ We made it into a square (of 33 and1/3 by adding a fourth מלבר, we will turn it back into a circle by reducing it a fourth, so the area of a circle with a diameter of 33 1/3 is the same that of a square which is 33 1/3 by 25, which is 833 1/3. ³⁶ The extra third is from the space of the tree, which has a diameter of 1/3. ³⁷ The אילן דמשנה (2500/3) is 833 and 1/3, and אילן דעולא (with the extra חצי אמה) is 33 1/3 in diameter whose area is also 833 1/3 (33.3333x33.3333=1111.10889 x.75=833.33). ³⁸ As in the ספרים דגרסי פלגא אמתא. ³⁹ 1089 x .75 = 816.75. ⁴⁰ 833 1/3 – 816 ¾ = 16 7/12. [1/3 = 4/12 + ¼ = 3/12 = 7/12.] ⁴¹ Let as assume that we first remove a strip half an אמה in the length, so we have a strip of 50 x ½. Then we remove a strip in the width. However since we already removed ½ אמה, the strip of the width now is only 49 ½ x ½ . we will add ¼ אמה to the 49 ½ from the 50 so we have two 49.75 strips each ½ אמה wide. Meaning we have a strip 49.75 x 1 אמה. ⁴² 49.75/3= 16 7/12. This is the amount that אילן דמשנה was greater than אילן דעולא (see [text by] footnote # 38). ⁴³ After subtracting 49.75 from a בית סאה (2500 square אמות) we have left 2450.25. That is the space required for 3 trees. Divide that by 3 (2450.25/3) = 816.75. The same amount a אילן דעולא. See footnote # 39.

לחומרא לא דק—He was not particular in being stringent

OVERVIEW We can infer from the ruling of עולא that if a tree is sixteen אמות away from the border he can bring ביכורים (but not less than sixteen אמות for then his tree nourishes from his neighbor’s field). The גמרא asked that based on the משנה a tree nourishes from more than a sixteen אמה radius,¹ so how can עלא obligate one to bring ביכורים from just a sixteen אמה radius. The גמרא explained that since עולא is being strict, he is obligating one to being ביכורים even from a sixteen אמה radius, he was not that exact. תוספות discusses this answer

תוספות asks: ואם תאמר והא נמי קולא הוא הא דמייתי ביכורים² דמפקע להו מתרומה ומעשר – And if you will say; but this ruling of עולא that he brings ביכורים if it is more than sixteen אמות, is also a leniency, for he exempts these ביכורים from תרומה and מעשר – כדאמרינן בהמוכר את הספינה³ (לקמן דף פא,ב ושם) – As the גמרא states in פרק המוכר את הספינה – תוספות answers: ויש לומר דעולא לא איירי אלא במאי דאינו מביא בתוך י"ו⁴ – And one can say that עולא is only discussing the issue that one does not bring ביכורים if the tree is within sixteen אמות –

However outside sixteen אמות, sometimes he brings ביכורים if it is**** as far as the proper שיעור mentioned in the משנה and sometimes he does not bring ביכורים, if it is more than sixteen but less than the שיעור of the משנה.

SUMMARY עולא never said that one brings ביכורים if it is (slightly more than) sixteen אמות.

THINKING IT OVER According to תוספות that עולא never said to bring ביכורים if it is sixteen אמות or more,⁵ what does the גמרא mean by saying ולחומרא לא דק, since עולא did not rule at all לחומרא, he merely ruled that less than sixteen one does not bring ביכורים?!⁶

footnotes: ¹ See previous תוס' ד"ה הכי whether it is 16 2/3 or 16 ½. ² According to עולא he will bring ביכורים if his tree is sixteen אמות away from his neighbor’s property, even though that he is really פטור from bringing ביכורים at that distance. However, he will not separate תרומות ומעשרות from the fruit that he is bringing as ביכורים, when in reality (since he is not חייב in ביכורים) he is obligated to separate תרו"מ from those 'ביכורים'. It turns out that by obligating him to bring ביכורים from a radius of sixteen, עולא is being lenient for he is exempting him from separating תרו"מ from those fruits. ³ ביכורים are not obligated in הפרשת תרו"מ since ביכורים itself is considered תרומה. ⁴ עולא merely stated that if the tree is within sixteen אמות he does not need to bring ביכורים. We are inferring that more than sixteen he is obligated; however, that inference may be mistaken. See ‘Thinking it over’. ⁵ See footnote # 3. ⁶ See מהר"ם.

אילן וקרקעו כולי—A tree and its land, etc.

OVERVIEW The גמרא challenges עולא (who maintains that one must have a radius of sixteen אמה around his tree on his property to bring ביכורים), from a משנה which states that if one bought a tree and its land he is obligated to bring ביכורים. The מקשן assumed that he needs to bring ביכורים even if it was a minuscule amount of land (less than sixteen אמות), which would contradict the ruling of עולא. The גמרא responded that the משנה (when it stated וקרקעו) means that he bought land in a sixteen אמה radius around the tree. תוספות discusses the need for such a ruling.

תוספות anticipates a difficulty: למאי דמוקי לה בי"ו אמה צריך לפרש מאי אתא לאשמועינן¹ – According to how the גמרא establishes this משנה that he bought sixteen אמות of land, it is necessary to explain what is this משנה coming to teach us?! תוספות responds: ונראה לרבינו שמשון בן אברהם דאתא לאשמועינן ולמידק – And it appears to the רשב"א that the משנה is coming to inform us that we should infer from this ruling – הא קנה אילן סתם אינו מביא וקורא – That if he simply bought one tree (without mentioning the land), he does not bring ביכורים and does not read the פרשה of ביכורים – ואם קנה ב' אפילו סתם מביא וקורא דקנה קרקע² – But if he bought two trees, even without mentioning the land around them, he brings ביכורים and reads פרשת ביכורים since he acquired the land – וכרבי מאיר דאמר³ (לקמן פא,א) הקונה ב' אילנות קנה קרקע: For this follows the ruling of ר"מ who maintains that one who buys two trees, he acquires the land around them.

SUMMARY The משנה may teach an obvious law in order that we should infer other laws from it.

THINKING IT OVER Does the משנה in ביכורים,⁴ support or contradict תוספות answer?

footnotes: ¹ It is obvious if he owns the tree and the land around it to nourish the tree, he certainly is required to bring ביכורים! ² The משנה when it states הקונה אילן וקרקעו מביא וקורא is not that much interested in this law (if we establish it where he bought sixteen אמות), but rather for the two inferences from the law, one that by one tree he brings ביכורים only if he explicitly bought the land around it, otherwise if nothing specific was mentioned regarding the land, we assume that he does not own the land and therefore אינו מביא, and two that it is only by one tree where he brings ביכורים only if he specifically negotiated to buy the land, however if he bought two trees, even if there was no discussion about the surrounding land, nevertheless he brings ביכורים, since this משנה agrees with ר"מ that when one buys two trees, he is קונה the קרקע (not like the חכמים who argue and maintain that only if he buys three trees is he קונה the קרקע). ³ See the משנה in ביכורים פ"א מי"א which states, הקונה שלשה אילנות בתוך של חברו, מביא וקורא, רבי מאיר אומר אפילו שניים, קנה אילן וקרקעו, מביא וקורא. See ‘Thinking it over’ ⁴ See footnote # 3.

הא שלשה מביא וקורא—However, three, he can bring and proclaim Overview¹ The גמרא cites a משנה which states² that if one bought two trees in his friend’s property, he may bring ביכורים, but does not read פרשת ביכורים. The implication is that if he bought three trees, he would be מביא וקורא, even if he owns a miniscule amount of land. This would contradict the ruling of עולא. Our תוספות examines the need for this inference.

תוספות anticipates a difficulty: הוה מצי למיפרך מסיפא³ דקתני בהדיא במסכת ביכורים בסיפא דהך דמייתי הכא – The גמרא could have challenged עולא from the סיפא for it was taught explicitly in מסכת ביכורים in the סיפא of this משנה, which was cited here, that הקונה ג' אילנות תוך של חבירו מביא וקורא⁴ – One who buys three trees within his friend’s property he is מביא וקורא – תוספות responds: אלא דאורחא דגמרא בכמה מקומות שמדקדק מרישא מה שיכול – Rather we need to say that it is the manner of the גמרא in many places to infer from the רישא as much as possible (even though it is explicit later in the סיפא).

SUMMARY Oftentimes the גמרא prefers to infer from the רישא what is explicit in the סיפא.

THINKING IT OVER Why did not תוספות ask that the גמרא could have challenged עולא from the רישא directly without any implication, since the רישא states that הקונה ב' אילנות מביא ואינו קורא, and we are assuming now that he only has קרקע כל שהוא, so why is he מביא according to עולא?!⁵

footnotes: ¹ See ‘Overview’ to the previous תוס' ד"ה אילן. ² מס' ביכורים פ"א משנה ו states; הקונה שני אילנות בתוך של חברו, מביא ואינו קורא. In משנה יא it states; הקונה שלשה אילנות בתוך של חברו, מביא וקורא. ³ סיפא here means משנה יא a few משניות after משנה ו' (which was cited here). See footnote # 2. ⁴ Why does the גמרא infer from the רישא when it states explicitly in the סיפא?! ⁵ See מהרש"א and נחלת משה.

לא שש עשרה אמה—No; sixteen cubits

OVERVIEW The גמרא concludes that there is no contradiction to עולא, for the משניות, which teach that he brings ביכורים, are all in cases where he owns sixteen אמות radius of land around the trees. תוספות clarifies this answer.

תוספות asks: ואם תאמר והא אמרינן בהמוכר את הספינה (לקמן דף פב,א ושם) גבי שלשה קנה קרקע – And if you will say; but ר' יוחנן states in פרק המוכר את הספינה regarding the משנה there¹ which rules that if he bought three trees he acquires the land around the trees – וכמה תחתיהן וביניהן וחוצה להן כמלא אורה וסלו² – And how much land is he קונה around the trees; he is קונה the land underneath the trees and the land between the three trees and outside the trees the amount of space necessary for the harvester and his basket – תוספות answers: ויש לומר דהתם כשענפי האילן גדולים הרבה ויוצאין חוץ לשש עשרה אמה³ – And one can say; that the גמרא there is in a case where the tree branches are very long and they extend beyond the sixteen אמה radius. תוספות asks: ואם תאמר קונה אילן אחד אמאי אינו מביא וקורא למאן דאמר קנין פירות כקנין הגוף דמי⁴ – And if you will say; one who buys one tree, why is he not מביא וקורא according to the one who maintains that ‘an acquisition for the fruits is just as an acquisition for the principal’ – ומאי שנא ממוכר שדהו לפירות – And why is this case of קונה אילן אחד different from one who sells his field for פירות – דמביא וקורא לדידיה כדאמרינן בפרק השולח (גיטין דף מז,ב ושם) – Where the rule is that the buyer is מביא וקורא as ר' יוחנן states in פרק השולח – תוספות anticipates and rejects a possible answer to his question: וליכא למימר דהאי תנא סבר דקנין פירות לאו כקנין הגוף דמי – And we cannot say that this תנא (who rules that הקונה אילן אחד is not מביא וקורא), maintains קנין פירות לאו כקנין הגוף דמי and therefore he is אינו מביא וקורא; this is not so – דהא רבי מאיר אית ליה דכקנין הגוף דמי בהשולח (שם דף מח,א) ובהחובל (בבא קמא דף צ,א ושם) – Since ר"מ maintains in פרק השולח and in פרק החובל that קנין פירות כקנין הגוף דמי – ואית ליה לקמן (דף פא,א) דקונה אילן אחד (אינו מביא וקורא⁵)⁶ – And nevertheless, he maintains later that one who buys one tree is מביא ואינו קורא – תוספות answers and distinguishes between קנין פירות elsewhere and here: ויש לומר דשאני התם שהקרקע קנוי לו עד זמן קבוע – And one can say that there (by a ‘regular’ קנין פירות) it is different than here, for there the land is acquired to him for a specific time, and during that agreed upon time the owner (seller) cannot renege – אבל הכא אם יתייבש מיד האילן אין לו בקרקע כלום – However here by the tree, if the tree would dry out immediately, he does not own anything in the land, he cannot even plant another tree there, therefore he is אינו קורא – אי נמי⁷ התם קרקע קנויה לו לכל דבר למשטח בה פירי ולמיזרע בה סילקא וירקא – Or you may also offer another difference; there the land is his (the buyer’s) to do anything with it, to spread out fruit on the land (to dry) or to plant there beets and vegetables – אבל גבי אילן אין לו אלא יניקה לבדה: However, regarding the tree, he only has the nourishment from the land, but he cannot use it for any other of his purposes.****

SUMMARY According to עולא, regular trees receive sixteen אמות; trees with branches that exceed 16 אמה receive an additional כמלא אורה וסלו. Even if we maintain קנין פירות כקנין הגוף דמי, nevertheless one who is קונה אילן אחד is not מביא וקורא, either because his קנין פירות could end immediately, or his rights are very limited.

THINKING IT OVER Is there a difference להלכה between the two answers⁸ תוספות gives regarding קנין פירות כקנין הגוף דמי?⁹

footnotes: ¹ פא,א. ² From the sגמרא' answer here it appears that when one buys three trees he acquires sixteen אמות radius around the tree; however from the גמרא there it appears that he receives (only) כמלא אורה וסלו, which is less than sixteen אמות. ³ In a ‘regular’ tree (where the branches extend less than sixteen אמה), the buyer receives just sixteen אמות. However, if the branches extend beyond sixteen אמות, he receives the entire area under the tree (which is more than sixteen אמה), plus כמלא אורה וסלו outside the tree to enable the harvester to pick the fruit. This is (only) according to עולא. ⁴ There is a dispute in the גמרא when one buys the rights to the fruits of a field (or the rent of a real estate property); meaning that all the fruits that grow belong to the buyer (but not to the owner of the field); does that make this buyer as if he is the owner of the field – קנין פירות כקנין הגף דמי, or not – קנין פירות לאו כקנין הגוף דמי. In our case this will make a difference whether הקונה אילן אחד is מביא וקורא or not. The owner of this tree has a קנין פירות in the field around the tree (even if he did not buy anything there, for it is self-understood when he bought this tree that it will be יונק from the surrounding area). Therefore, if we maintain קנין פירות כקנין הגוף דמי, the owner of the tree ‘owns’ the nourishing area, so it is מארצך and מן האדמה שנתת לי, etc. He. therefore, should be obligated to bring ביכורים. ⁵ A marginal note amends this to read מביא ואינו קורא (instead of אינו מביא וקורא). ⁶ The question then is on ר"מ, since he maintains קנין פירות כקנין הגוף דמי why is he אינו קורא?! ⁷ See ‘Thinking it over’. ⁸ See footnote # 7. ⁹ See נחלת משה.

ובוידוי¹—And with confession

OVERVIEW רבי עקיבא stated that even a minuscule amount of land obligates a person with certain responsibilities (including פאה and ביכורים, etc.). תוספות cites רש"י that we are not גורס the word 'ובוידוי' and discusses it.

פירוש בקונטרס² דלא גרסינן ובוידוי דלא כתיב במעשר שני (שיש) שום וידוי³ – רש"י explained that the text does not read 'ובוידוי', for by the וידוי of מעשר שני it is not written – לא מארצך ולא מאדמה אשר נתת לי⁴ – Neither מארצך (from your land) nor מאדמה אשר נתת לי (from the land which you gave me) – תוספות responds to an anticipated difficulty: אף על גב דכתיב ביה וברך את עמך את ישראל ואת האדמה אשר נתתה לנו (דברים כו⁵) – Even though it says by וידוי מעשר, ‘and bless your nation ישראל and the land which you gave us’, which may seemingly indicate that one must own the land – לא שיהא לו לחלק אלא לכל ישראל – It does not mean that he (the individual) should have a portion (ownership) in the land, rather the land which ה' gave us, which belongs to all of ישראל (but not that it belongs to this particular person). According to רש"י (as תוספות explains it) there is no need to own קרקע in order to proclaim וידוי מעשר. However תוספות cites a dissenting view: ומיהו על כרחך אין וידוי בלא קרקע דתני עלה בירושלמי⁶ אף בוידוי⁷ – Nevertheless, perforce you must say that there can be no וידוי מעשר without owning land, for it was taught in the תלמוד ירושלמי, on this משנה of ר"ע, that also by וידוי we require קרקע כל שהוא.

But nevertheless (even though וידוי requires קרקע) we are not גורס וידוי in the משנה (of ר"ע), for since it was taught in the גמרא of the ירושלמי, it is evident that in the משנה there is no mention of וידוי (otherwise why does the גמרא there need to mention it).

SUMMARY Both רש"י and תוספות agree that we are not גורס the word וידוי in the משנה; however according to רש"י it does not require קרקע, while according to תוספות (based on the ירושלמי) it does require קרקע כ"ש.

THINKING IT OVER Is the reason תוספות offers why וידוי does not require קרקע the same reason which רש"י gives,⁸ or is it different?

footnotes: ¹ וידוי here refers to the proclamation one makes concerning his distribution of מעשרות. This is found in דברים (תבא) כו,יג-טו. It is known as וידוי מעשרות. ² בד"ה ובוידוי. In our רש"י it states דאין וידוי אלא במעשר והוא אינו תלוי בקרקע. See ‘Thinking it over’. ³ The הגהות פורת יוסף amends this to read דלא כתיב בוידוי מעשר שני לא (instead of דלא כתיב במעשר שני (שיש) שום וידוי). ⁴ If it would say (by וידוי מעשר) the word מארצך, or האדמה אשר נתת לי (as it says by ביכורים), it would have the same ruling as ביכורים that it must be from your land, and according to עולא it would require the sixteen אמות in order not to be יונק משדה חבירו, however since these words do not appear by וידוי מעשרות, there is no such requirement (to have any land at all). ⁵ פסוק טו. ⁶ פאה פ"ג ה"ו. In our ירושלמי it is on יז,ב. ⁷ תוספות disagrees with רש"י (based on the ירושלמי) and maintains that וידוי מעשר requires קרקע. ⁸ See footnote 2.

ולכתוב עליה פרוזבול—And to write a Prusbul on it

OVERVIEW ר"ע ruled that in order to write a פרוזבול,¹ the לוה must have some קרקע, even a miniscule amount is sufficient. תוספות discuses this ruling

אבל אמטלטלין אין כותבין פרוזבול מפני שיכול לכלותן והיא הלואה דלא שכיחא² – However, if the borrower owns only movable items, we do not write a פרוזבול, since the לוה can rid himself from them, so it is an uncommon type of loan – ועציץ נקוב³ אף על פי שיכול לכלותו כותבין עליו פרוזבול דלא פלוג רבנן במקרקעי – And regarding a perforated flowerpot, one may write a פרוזבול if the לוה owns one. Even though it can be destroyed, nevertheless the רבנן did not distinguish between different types of קרקע – תוספות anticipates a difficulty: והא דכותבין אפילו על קרקע כל שהוא⁴ – And the reason we write a פרוזבול even on a miniscule amount of land – תוספות responds: פירש רבינו שמואל בן מאיר בהשולח (גיטין דף לז,א דיבור המתחיל אלא) משום דאין אונאה לקרקעות – The רשב"ם explained in פרק השולח, since there is no ‘cheating’⁵ by קרקעות – והוי כאילו יש לו משכון בכל⁶ – So therefore, it is considered as if he has collateral for the entire loan – תוספות disagrees: ואין נראה דנהי דאין להן אונאה ביטול מקח ביתר מפלגא יש להן⁷ – And this answer does not appear to be correct, for granted that קרקע is not subject to the regular rules of אונאה, nevertheless the sale can be annulled if it is sold for more than half its market value – תוספות offers his interpretation: אלא היינו טעמא משום דגבי והדר גבי כמעשה דקטינא דאביי⁸ (כתובות דף צא,ב) – Rather this is the reason that we write a פרוזבול on קרקע כ"ש, because he can collect and collect again, like the story of אביי with a small plot of land – דעל ידי כך ראוי לגבות כל חובו וכענין זה איכא סוף פרק כל הגט (גיטין דף ל,ב) – That through this process it is possible to collect the entire debt. And there is something similar to this in the end of פרק כל הגט – גבי המלוה מעות את הכהן כולי⁹ הניח מלא מחט גובה מלא קורדום: Regarding one who lends money to a כהן, etc. that if he left over land even the size of a needle, he can collect the size of an axe

SUMMARY We cannot write a פרוזבול for מטלטלין; however, we write for קרקע כ"ש either because אין אונאה לקרקעות, or because we can collect it repeatedly.

THINKING IT OVER תוספות writes that we do not write a פרוזבול on מטלטלין because it is a מילתא דלא שכיחא.¹⁰ If that is the case, why can we write a פרוזבול on a קרקע כ"ש; seemingly there too it is a מילתא דלא שכיחא to lend money to someone who virtually has no קרקע?!¹¹

footnotes: ¹ See רש"י ד"ה פרוזבול, that this is a תקנה of הלל that the lender assigns his debts to בי"ד so that the מלוה should be able to collect them even after שמיטה. ² A מלוה is usually only willing to lend when the לוה owns קרקע, for then his loan is secured by the land, however if the לוה has only מטלטלין (but no land), the loan is not secured, for the מטלטלין can be lost or stolen or sold, etc. Therefore, since this is an uncommon case, the חכמים did not institute their תקנות by a מילתא דלא שכיחא. See ‘Thinking it over’. ³ Plants that grow in an עציץ נקוב are considered (מחובר ל)קרקע regarding many laws, since they nourish from the ground through the hole(s) in the עציץ (נקוב). ⁴ A קרקע כ"ש will (seemingly) not be sufficient to secure the loan; why is it different from מטלטלין?! ⁵ The rule of אונאה is that if an item was overcharged (or undercharged) by a sixth or more, there is recourse; the sale is nullified if the difference was more than a sixth, or if it was exactly a sixth, the amount overpaid (or underpaid) must be returned to the buyer (or seller). However, by קרקע even if one was overcharged by more than a sixth, the sale is valid as is. This means that a piece of קרקע which has a certain market value, can be considered to be worth much more, since if you sell at a much higher price, the sale will be valid. ⁶ The small piece of land, which the לוה has, can be considered to be worth much more (the entire amount of the loan), since the מלוה can collect it and sell it for a much higher price; therefore his loan is secured. ⁷ See כתובת צט,ב ואילך. This means that if land which was worth one hundred was sold for (more than) two hundred, the sale is void. Therefore, if the loan is much more than the value of this קרקע כ"ש how can it be considered as collateral, and so the פרוזבול should not be effective. ⁸ The story there is that a לוה owed two hundred זוז, and he passed on and left over a small plot of land worth fifty זוז. The מלוה took that field as partial payment for his loan. The heirs of the לוה came and gave him fifty זוז and reclaimed the field. The מלוה went back and took the field again since his loan was not paid up and this land is משועבד for the loan. אביי ruled there that the מלוה has the right to do so, עיי"ש. Here too the מלוה can collect this small parcel for partial payment and then when the לוה will redeem his field (by paying the מלוה its value), the מלוה can go back and take the field again and again until his loan is fully paid. ⁹ The משנה there (on ל,א) teaches that one may lend money to a כהן, etc. and receive payment by keeping the תרומה, which he is normally required to give to a כהן, and deduct it from the money owed to him by the כהן. The גמרא there states that if the כהן died and left over land (which is משעובד for his loan), he may (according to ר' יוחנן) continue to collect his full debt (by keeping the תרומה) even if the land was very small (כמלא מחט), since whenever the יורשים choose to redeem the field, he can again claim the field which is משועבד to him (so potentially he has a שעבוד for his entire loan). ¹⁰ See footnote # 2. ¹¹ See נחלת משה.