The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 13
... fore AB is not unequal to AC , that is , it is equal to it . Where- fore , if two angles , & c . Q. E. D. B DA COR . Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . Upon the same base , and on the same side ...
... fore AB is not unequal to AC , that is , it is equal to it . Where- fore , if two angles , & c . Q. E. D. B DA COR . Hence every equiangular triangle is also equilateral . PROP . VII . THEOR . Upon the same base , and on the same side ...
Page 15
... to the base EF ; there- + Const . fore the angle DAF is equal to the angle EAF : * 8 . 1 . wherefore the given rectilineal angle BAC is * 1 . 1 . * 9 . 1 . C 2 BOOK I. PROP . IX . 15 gle ABC be applied to DEF, so that the ...
... to the base EF ; there- + Const . fore the angle DAF is equal to the angle EAF : * 8 . 1 . wherefore the given rectilineal angle BAC is * 1 . 1 . * 9 . 1 . C 2 BOOK I. PROP . IX . 15 gle ABC be applied to DEF, so that the ...
Page 16
... fore the base AD is equal to the A * 4.1 . * 3.1 . * 1 . 1 . † Const . * D B base DB , and the straight line AB is divided into two equal parts in the point D. Which was to be done . PROP . XI . PROB . To draw a straight line at right ...
... fore the base AD is equal to the A * 4.1 . * 3.1 . * 1 . 1 . † Const . * D B base DB , and the straight line AB is divided into two equal parts in the point D. Which was to be done . PROP . XI . PROB . To draw a straight line at right ...
Page 23
... fore AC is greater than AB . greater angle , & c . Q. E. D. Wherefore the PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any two sides of it together shall be greater ...
... fore AC is greater than AB . greater angle , & c . Q. E. D. Wherefore the PROP . XX . THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any two sides of it together shall be greater ...
Page 28
... fore the base GC is equal to the base DF , and the triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite : therefore the angle 28 EUCLID'S ELEMENTS .
... fore the base GC is equal to the base DF , and the triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite : therefore the angle 28 EUCLID'S ELEMENTS .
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