The Elements: Books III-IXSt. John's College Press, 1949 - Mathematics, Greek |
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Page 195
... parallels . Therefore DE is parallel to BC . Therefore etc. Q. E. D. [ 1. 39 ] Euclid evidently did not think it worth while to distinguish in the enunciation , or in the figure , the cases in which the parallel to the base cuts the ...
... parallels . Therefore DE is parallel to BC . Therefore etc. Q. E. D. [ 1. 39 ] Euclid evidently did not think it worth while to distinguish in the enunciation , or in the figure , the cases in which the parallel to the base cuts the ...
Page 231
... parallel to DE , meeting CE , produced if necessary , in E , EF ' parallel to EF , meeting CF , produced if necessary , in F , and so on . Let the parallel to the last side but one , FG , meet CG , produced if necessary , in G ' . Then ...
... parallel to DE , meeting CE , produced if necessary , in E , EF ' parallel to EF , meeting CF , produced if necessary , in F , and so on . Let the parallel to the last side but one , FG , meet CG , produced if necessary , in G ' . Then ...
Page 272
Euclid Sir Thomas Little Heath. ABC is a triangle . From C draw CD parallel to BA and of any length . From D draw DE parallel to CA and of such length that CD : DE BA : AC . = E Then the triangles ABC , ECD , which have the angular point ...
Euclid Sir Thomas Little Heath. ABC is a triangle . From C draw CD parallel to BA and of any length . From D draw DE parallel to CA and of such length that CD : DE BA : AC . = E Then the triangles ABC , ECD , which have the angular point ...
Common terms and phrases
ABCD angle ABC angle BAC antecedent Aristotle base bisected centre circle ABC circumference construction continued proportion corresponding sides cube number definition diameter drawn enunciation equal angles equiangular equimultiples Euclid Eutocius ex aequali four magnitudes geometrical geometrical progression given circle given straight line greater ratio greatest common measure Heiberg hypothesis Iamblichus joined less mean proportional numbers measures the number multiple multitude Nicomachus odd number parallel parallelogram pentagon perpendicular polygon Porism prime number Proclus Prop proper fraction proposition PROPOSITION 13 proved rect rectangle rectangle contained rectilineal figure reductio ad absurdum remaining angle right angles segment semicircle similar and similarly similar plane numbers Simson solid numbers square number subtracted taken Theon Theon of Smyrna theorem touches the circle triangle ABC unit VIII δὲ καὶ πρὸς τὸ τοῦ