The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 13
... 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 of it , there cannot be two triangles that have their sides , which are terminated in one ...
... 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 of it , there cannot be two triangles that have their sides , which are terminated in one ...
Page 14
... Q. E. D. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to ...
... Q. E. D. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to ...
Page 19
... Q. E. D. PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the ...
... Q. E. D. PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the ...
Page 20
... Q. E. D. PROP . XV . THEOR . If two straight lines cut one another , the vertical , or opposite angles , shall be equal . Let the two straight lines AB , CD , cut one another in the point E : the angle AEC shall be equal to the angle ...
... Q. E. D. PROP . XV . THEOR . If two straight lines cut one another , the vertical , or opposite angles , shall be equal . Let the two straight lines AB , CD , cut one another in the point E : the angle AEC shall be equal to the angle ...
Page 21
... Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together shall be less than two right angles . B Produce BC to D ; and be- cause ACD ...
... Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together shall be less than two right angles . B Produce BC to D ; and be- cause ACD ...
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