The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfthF. Wingrave, 1804 |
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Página 32
... reason , EF is equal to BC ; wherefore AD is h . 1 , Ax . equal to EF ; and DE is common ; therefore the whole , or the 1 . C c 2. or 3. remainder , AE is equal to the whole , or the remainder DF ; AB alfo is equal to DC ; and the two ...
... reason , EF is equal to BC ; wherefore AD is h . 1 , Ax . equal to EF ; and DE is common ; therefore the whole , or the 1 . C c 2. or 3. remainder , AE is equal to the whole , or the remainder DF ; AB alfo is equal to DC ; and the two ...
Página 33
... reason the parallelogram EFGH is equal to the fame EBCH . therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. TRI PROP . XXXVII . THEOR . RIANGLES upon the same base , and between the fame ...
... reason the parallelogram EFGH is equal to the fame EBCH . therefore also the parallelogram ABCD is equal to EFGH . Wherefore parallelograms , & c . Q. E. D. TRI PROP . XXXVII . THEOR . RIANGLES upon the same base , and between the fame ...
Página 37
... reason , the triangle KGC is equal to the triangle KFC . then because the triangle A EK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK together with the triangle KGC is equal to the triangle AHK together ...
... reason , the triangle KGC is equal to the triangle KFC . then because the triangle A EK is equal to the triangle AHK , and the triangle KGC to KFC ; the triangle AEK together with the triangle KGC is equal to the triangle AHK together ...
Página 41
... reason , AB and AH are in the fame ftraight line . and because the angle DBC is equal to the angle FBA , each of them being a right angle , add to each the angle ABC , and the whole angle DBA is B G Book I. b . 31. I. C. 30. Def . H K d ...
... reason , AB and AH are in the fame ftraight line . and because the angle DBC is equal to the angle FBA , each of them being a right angle , add to each the angle ABC , and the whole angle DBA is B G Book I. b . 31. I. C. 30. Def . H K d ...
Página 50
... reason PR is equal to RO . and because CB is equal to BD , C. 43. I. C b . 36. 1. and GK to KN , the rectangle CK is equal to BN , and GR to RN . but CK is equal to RN , because they are the complements of the parallelogram CO ...
... reason PR is equal to RO . and because CB is equal to BD , C. 43. I. C b . 36. 1. and GK to KN , the rectangle CK is equal to BN , and GR to RN . but CK is equal to RN , because they are the complements of the parallelogram CO ...
Términos y frases comunes
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone conſtruction cylinder defcribed demonſtrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fecond fegment fhall fhewn fides fides BA fimilar fince firft firſt folid angle fore fquare fquare of AC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular plane angles PROP Propofition pyramid rectangle contained rectilineal figure right angles ſame ſhall ſpace ſphere ſquare ſtraight line AB THEOR theſe thro tiple triangle ABC wherefore
Pasajes populares
Página 157 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.
Página 24 - ... be equal, each to each ; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, ECA equal to the angles DEF, EFD, viz.
Página 45 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Página 163 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 81 - ELF. Join BC, EF ; and because the circles ABC, DEF are equal, the straight lines drawn from their centres are equal: therefore the two sides BG, GC, are equal to the two EH, HF ; and the angle at G is equal to the angle at H ; therefore the base BC is equal (4.
Página 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Página 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.