The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . 10 EUCLIDS ELEMENTS. For if the triangle ABC be applied to the triangle DEF,so that the point A may be on the point D, and thestraight Hne AB on thestraight line DE, thepoint B will coincide withthe point E, because ABis equal to DE. {, AB coinciding with DE, ^(7 will fall on DF, because the angle BAG ^ C E P is equal to the angle EDF. [Hypothesis. Therefore also the point G will coincide with the point F,because ^C is equ
The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . 10 EUCLIDS ELEMENTS. For if the triangle ABC be applied to the triangle DEF,so that the point A may be on the point D, and thestraight Hne AB on thestraight line DE, thepoint B will coincide withthe point E, because ABis equal to DE. {, AB coinciding with DE, ^(7 will fall on DF, because the angle BAG ^ C E P is equal to the angle EDF. [Hypothesis. Therefore also the point G will coincide with the point F,because ^C is equal to DF. {Hypothesis. But the point B was shewn to coincide with the point E,therefore the base BG will coincide with the base EF;because, B coinciding with E and G with F, if the base BGdoes not coincide with the base EF, two straight Hues willenclose a space ; which is impossible. {Axiom 10. Therefore the base BG coincides with the base EF, and isequal to it. {Axiom 8. Therefore the whole triangle ABG coincides with the wholetriangle DEF, and is equal to it. {Axiom 8. And the other angles of the one coincide with the otherangles of the other, and are equal
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