The Elements of Plane and Solid Geometry |
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Page 9
... DEF , its shape remaining unaltered , it would follow that the portion of superficial space ABC was , as to shape and size , exactly identical with the portion DEF . A D B E с F In such a case as this we often speak of transferring the ...
... DEF , its shape remaining unaltered , it would follow that the portion of superficial space ABC was , as to shape and size , exactly identical with the portion DEF . A D B E с F In such a case as this we often speak of transferring the ...
Page 14
... ABC and DBC , having the two sides BA and BD , terminated in B , equal to each other , and at the same time the two ... Def . 20. - A triangle is said to have six parts - three sides and three angles , and two triangles are said to be ...
... ABC and DBC , having the two sides BA and BD , terminated in B , equal to each other , and at the same time the two ... Def . 20. - A triangle is said to have six parts - three sides and three angles , and two triangles are said to be ...
Page 15
... ABC and DEF be two triangles , having the two sides BA and AC equal to the two sides ED and DF each to each , and the angle BAC equal to the angle EDF , then shall BC be equal to EF , and the angles ABC and ACB to DEF and DFE , each to ...
... ABC and DEF be two triangles , having the two sides BA and AC equal to the two sides ED and DF each to each , and the angle BAC equal to the angle EDF , then shall BC be equal to EF , and the angles ABC and ACB to DEF and DFE , each to ...
Page 16
... ABC and DEF are equal in all their parts . Next let the triangle DEF be situated as in Fig . 8 . In this case when AB coincides with DE , AC and DF must lie on opposite sides of DE unless the plane of the triangle ABC be reversed so ...
... ABC and DEF are equal in all their parts . Next let the triangle DEF be situated as in Fig . 8 . In this case when AB coincides with DE , AC and DF must lie on opposite sides of DE unless the plane of the triangle ABC be reversed so ...
Page 17
... ABC and DEF be two triangles , having the two angles ABC and ACB of the one , respectively , equal to the two angles DEF and DFE of the other , and the side BC equal to the side EF , then shall the two triangles be equal in all their ...
... ABC and DEF be two triangles , having the two angles ABC and ACB of the one , respectively , equal to the two angles DEF and DFE of the other , and the side BC equal to the side EF , then shall the two triangles be equal in all their ...
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Common terms and phrases
ABC and DEF ABCD adjacent angles angle ABC angle ACB angle BAC BC is equal centre circumference coincide common measure construction Corollary diameter dicular dihedral angle distance divided equal angles equal to AC equidistant exterior angle figure four right angles given angle given circle given plane given point given ratio given straight line greater homologous inscribed intersecting straight lines length less Let ABC line of intersection locus magnitudes meet the circle middle point multiple number of sides opposite sides parallelogram pentagon perpen perpendicular plane AC point F produced Prop PROPOSITION PROPOSITION 13 Prove radii radius rectangle regular polygon respectively equal rhombus right angles segments side BC similar triangles Similarly situated square straight line AB straight line BC subtended tangent triangle ABC triangle DEF
Popular passages
Page 15 - If two triangles have two sides of the one equal to two sides of the...
Page 101 - Through a given point to draw a straight line parallel to a given straight line. Let A be the given point, and BC the given straight line, it is required to draw a straight line through the point A, parallel to the line BC.
Page 126 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 222 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Page 188 - If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Page 204 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 14 - 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 other extremity.
Page 12 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Page 161 - Ir there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words