The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 10
... base BC shall coincide with the base EF : because , the point B coinciding with E , and C with F , if the base BC does not coin- cide with the base EF , two straight lines would 10 Ax . inclose a space , which is impossible . * Therefore ...
... base BC shall coincide with the base EF : because , the point B coinciding with E , and C with F , if the base BC does not coin- cide with the base EF , two straight lines would 10 Ax . inclose a space , which is impossible . * Therefore ...
Page 11
... base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight ... base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the re- maining angles of the one ...
... base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight ... base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the re- maining angles of the one ...
Page 12
... base of the triangle ABC : and it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base , & c . Q. E. D. 3.1 . COROLLARY . - Hence ...
... base of the triangle ABC : and it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base , & c . Q. E. D. 3.1 . COROLLARY . - Hence ...
Page 13
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle * ACB , the less to the greater , which is absurd . There- fore AB is not unequal to AC , that is , it is equal to it . Where- fore , if two angles , & c ...
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle * ACB , the less to the greater , which is absurd . There- fore AB is not unequal to AC , that is , it is equal to it . Where- fore , if two angles , & c ...
Page 14
... base CD are equal to one another : but the 19 Ax . angle ECD is greater than the angle BCD : wherefore the angle FDC ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
... base CD are equal to one another : but the 19 Ax . angle ECD is greater than the angle BCD : wherefore the angle FDC ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole