Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
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Page 22
... equilateral triangle upon a given finite straight line Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the distance AB , describe ( 3. Pos- tulate ) the circle BCD ...
... equilateral triangle upon a given finite straight line Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the distance AB , describe ( 3. Pos- tulate ) the circle BCD ...
Page 25
... equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which sub- tend , or are opposite to them , are also equal to one another . Let ABC be a triangle having the ...
... equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which sub- tend , or are opposite to them , are also equal to one another . Let ABC be a triangle having the ...
Page 51
... equilateral ; it is likewise rectangular ; for the straight line AD meeting the parallels , AB , DE , makes the angles BAD , ADE equal ( 29 . 1. ) to two right angles ; but BAD is a right angle ; therefore also ADE is a right angle now ...
... equilateral ; it is likewise rectangular ; for the straight line AD meeting the parallels , AB , DE , makes the angles BAD , ADE equal ( 29 . 1. ) to two right angles ; but BAD is a right angle ; therefore also ADE is a right angle now ...
Page 101
... equilateral decagon inscrib- " ed in the circle BDE . " PROP . XI . PROB . To inscribe an equilateral and equiangular pentagon in a given circle . Let ABCDE be the given circle , it is required to inscribe an equi- lateral and ...
... equilateral decagon inscrib- " ed in the circle BDE . " PROP . XI . PROB . To inscribe an equilateral and equiangular pentagon in a given circle . Let ABCDE be the given circle , it is required to inscribe an equi- lateral and ...
Page 102
... equilateral . Wherefore , in the given circle , an equilateral and equiangular pentagon has been in- scribed . Which was to be done . : Otherwise . " Divide the radius of the given circle , so that the rectangle con- " tained by the ...
... equilateral . Wherefore , in the given circle , an equilateral and equiangular pentagon has been in- scribed . Which was to be done . : Otherwise . " Divide the radius of the given circle , so that the rectangle con- " tained by the ...
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Common terms and phrases
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line BD THEOR third touches the circle triangle ABC triangle DEF wherefore