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 TrigonometryJ.B. Lippincott, 1857 - 317 σελίδες |
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Σελίδα 13
... bases , or third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be ... base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are ...
... bases , or third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be ... base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are ...
Σελίδα 14
... base BC shall coincide with the base EF cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
... base BC shall coincide with the base EF cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
Σελίδα 15
... base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a ... base DC is equal to the base AB , and the area of the triangle DBC is equal to that of the triangle ( 4. 1. ) ACB , the ...
... base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a ... base DC is equal to the base AB , and the area of the triangle DBC is equal to that of the triangle ( 4. 1. ) ACB , the ...
Σελίδα 16
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
Σελίδα 17
... base EF , side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ; but this is ...
... base EF , side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ; but this is ...
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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 plane 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 third touches the circle triangle ABC triangle DEF wherefore