Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 45
... draw ( 31. 1. ) BE parallel to CA ; and through C draw CF parallel to BD : Therefore , each of the figures EBCA , DBCF is a paral- E B A D lelogram ; and DBCA is equal ( 35. 1. ) to DBCF , because they are upon the same base BC , and ...
... draw ( 31. 1. ) BE parallel to CA ; and through C draw CF parallel to BD : Therefore , each of the figures EBCA , DBCF is a paral- E B A D lelogram ; and DBCA is equal ( 35. 1. ) to DBCF , because they are upon the same base BC , and ...
Página 46
... draw BG parallel ( 31. 1. ) to CA , and through F draw FH parallel to ED : Then each of the figures GBCA , DEFH is a paral- lelogram ; and they are equal to ( 36. 1. ) one an- other , because they are upon equal bases BC , EF and ...
... draw BG parallel ( 31. 1. ) to CA , and through F draw FH parallel to ED : Then each of the figures GBCA , DEFH is a paral- lelogram ; and they are equal to ( 36. 1. ) one an- other , because they are upon equal bases BC , EF and ...
Página 47
... draw ( 31. 1. ) AG parallel to BF , and join GF . The triangle ABC is equal ( 38. 1. ) to the triangle GEF , because they are upon equal bases BC , EF , and between the same parallels BF , AG : But the tri- angle ABC is equal to the ...
... draw ( 31. 1. ) AG parallel to BF , and join GF . The triangle ABC is equal ( 38. 1. ) to the triangle GEF , because they are upon equal bases BC , EF , and between the same parallels BF , AG : But the tri- angle ABC is equal to the ...
Página 48
... draw ( 31. 1. ) AG parallel to BC , and through C draw CG ( 31. 1. ) parallel to EF : Therefore FECG is a parallelogram : And because A BE is equal to EC , the triangle ABE is likewise equal ( 38. 1. ) to the triangle AEC , since they ...
... draw ( 31. 1. ) AG parallel to BC , and through C draw CG ( 31. 1. ) parallel to EF : Therefore FECG is a parallelogram : And because A BE is equal to EC , the triangle ABE is likewise equal ( 38. 1. ) to the triangle AEC , since they ...
Página 49
... draw ( 31. 1. ) AH parallel to BG or EF , and join HB . Then because the straight line HF falls upon the parallels AH , EF , the angles AHF , HFE , are together equal ( 29. 1. ) to two right angles ; wherefore the angles BHF , HFE are ...
... draw ( 31. 1. ) AH parallel to BG or EF , and join HB . Then because the straight line HF falls upon the parallels AH , EF , the angles AHF , HFE , are together equal ( 29. 1. ) to two right angles ; wherefore the angles BHF , HFE are ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore