The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 8
... triangle upon a given finite straight line . Let AB be the given straight line ; it is re- quired to describe an ... ABC shall be an equilateral triangle . finition . Because the point A is the centre of the circle * 15 De- BCD , AC is ...
... triangle upon a given finite straight line . Let AB be the given straight line ; it is re- quired to describe an ... ABC shall be an equilateral triangle . finition . Because the point A is the centre of the circle * 15 De- BCD , AC is ...
Page 10
... ABC , DEF be two triangles , which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz ... triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite , shall be equal each to ...
... ABC , DEF be two triangles , which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz ... triangle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite , shall be equal each to ...
Page 11
... ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal to ... triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be ...
... ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal to ... triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be ...
Page 12
... triangle ABC : and it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon ... triangle be equal to one another , the sides also which subtend or are oppo- site to the equal angles , shall be ...
... triangle ABC : and it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon ... triangle be equal to one another , the sides also which subtend or are oppo- site to the equal angles , shall be ...
Page 14
... triangle ACB ; produce AC , AD to E , F Hyp . therefore , because AC is ... ABC , DEF be two triangles , having the two sides AB , AC equal to the two ... ABC be applied to DEF , so that the 14 EUCLID'S ELEMENTS .
... triangle ACB ; produce AC , AD to E , F Hyp . therefore , because AC is ... ABC , DEF be two triangles , having the two sides AB , AC equal to the two ... ABC be applied to DEF , so that the 14 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