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 TrigonometryW. E. Dean, 1840 - 317 σελίδες |
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Σελίδα 12
... triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle ... ABC is an equilateral triangle . Because the point A is the cen- tre of the circle BCD , AC is equal ...
... triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle ... ABC is an equilateral triangle . Because the point A is the cen- tre of the circle BCD , AC is equal ...
Σελίδα 13
... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB ... triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , B E F viz ...
... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB ... triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , B E F viz ...
Σελίδα 14
... ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ; and the remaining angles of the one shall coincide with the remaining angles of the ... triangle ABC : And it has 14 ELEMENTS.
... ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ; and the remaining angles of the one shall coincide with the remaining angles of the ... triangle ABC : And it has 14 ELEMENTS.
Σελίδα 15
... triangle ABC : And it has also been proved ... triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC ...
... triangle ABC : And it has also been proved ... triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC ...
Σελίδα 16
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ... ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB ...
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ... ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore