The Thirteen Books of Euclid's Elements ; The Works of Archimedes, Including the Method ; Introduction to Arithmetic |
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Page 185
... PROPOSITION 24 If from an even number an even number be subtracted , the remainder will be even . For from the even number AB let the even number BC be subtracted : I say that the remainder CA is even . A c B For , since AB is even , it ...
... PROPOSITION 24 If from an even number an even number be subtracted , the remainder will be even . For from the even number AB let the even number BC be subtracted : I say that the remainder CA is even . A c B For , since AB is even , it ...
Page 468
... proposition . ( 2 ) If any conoid or spheroid be cut by a plane through the axis , and if through any tangent to the resulting conic a plane be erected at right angles to the plane of section , the plane so erected will touch the conoid ...
... proposition . ( 2 ) If any conoid or spheroid be cut by a plane through the axis , and if through any tangent to the resulting conic a plane be erected at right angles to the plane of section , the plane so erected will touch the conoid ...
Page 488
... proposition is given above , pp . 456-7 , and it is there pointed out that the result is equivalent to 12 + 22 + 32 + ยทยทยท + n2 = n ( n + 1 ) ( 2n + 1 ) - . ] 6 COR . 1. It follows from this proposition that and also that n A2 < 3 ( A1 + ...
... proposition is given above , pp . 456-7 , and it is there pointed out that the result is equivalent to 12 + 22 + 32 + ยทยทยท + n2 = n ( n + 1 ) ( 2n + 1 ) - . ] 6 COR . 1. It follows from this proposition that and also that n A2 < 3 ( A1 + ...
Common terms and phrases
angle ABC angle BAC apotome axis base BC is equal binomial straight line bisected centre of gravity circle ABCD circumference circumscribed commensurable in length commensurable in square cone continued proportion cube cylinder diameter double equal angles equiangular equilateral equimultiples figure fluid frustum gnomon height incommensurable inscribed joined less let the square magnitudes mean proportional medial area medial straight line multiplying parabola paraboloid parallelogram pentagon perpendicular plane of reference polygon prime prism produced Prop PROPOSITION 13 proved pyramid Q. E. D. PROPOSITION radius rational straight line rectangle AC rectangle contained remaining angle right angles side similar Similarly sphere spheroid square number square on AB squares on AC straight lines commensurable superparticular surface tangent triangle ABC twice the rectangle vertex whole