The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 11
... THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB ...
... THEOR . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB ...
Page 13
... 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 extremity of the base , equal to one another , and likewise those which are terminated in the ...
... 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 extremity of the base , equal to one another , and likewise those which are terminated in the ...
Page 18
... THEOR . The angles which one straight line makes with another upon one side of it , are either two right angles , or are together equal to two right angles . Let the straight line AB make with CD , upon one side of it , the angles CBA ...
... THEOR . The angles which one straight line makes with another upon one side of it , are either two right angles , or are together equal to two right angles . Let the straight line AB make with CD , upon one side of it , the angles CBA ...
Page 21
... THEOR . If one side of a triangle be produced , the exterior angle is greater than either of the interior op- posite angles .. Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be greater than ...
... THEOR . If one side of a triangle be produced , the exterior angle is greater than either of the interior op- posite angles .. Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be greater than ...
Page 22
... THEOR . * The greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB : " the angle ABC shall be greater than the angle BCA . " 2 • Because AC is greater ...
... THEOR . * The greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB : " the angle ABC shall be greater than the angle BCA . " 2 • Because AC is greater ...
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