The Elements of Plane and Solid GeometryLongmans, Green, and, Company, 1871 - 285 páginas |
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Página 13
... Similarly CE + ED is greater than CD , therefore AE + EB ÷ CE + ED is greater than AB + CD . But AE + CE is equal to AC , and EB + ED is equal to DB , therefore AC + DB is greater than AB + DC . PROPOSITION 4 . Upon the same base and on ...
... Similarly CE + ED is greater than CD , therefore AE + EB ÷ CE + ED is greater than AB + CD . But AE + CE is equal to AC , and EB + ED is equal to DB , therefore AC + DB is greater than AB + DC . PROPOSITION 4 . Upon the same base and on ...
Página 15
... is equal to the straight line EF . ( Ax . 1 and Def . 6. ) And because AB coincides with DE and BC with EF the angle ABC is equal to the angle DEF . ( Def . 11. ) Similarly the angle ACB is equal to the angle DFE Triangles . 15.
... is equal to the straight line EF . ( Ax . 1 and Def . 6. ) And because AB coincides with DE and BC with EF the angle ABC is equal to the angle DEF . ( Def . 11. ) Similarly the angle ACB is equal to the angle DFE Triangles . 15.
Página 16
Henry William Watson. Similarly the angle ACB is equal to the angle DFE ; there- fore the triangles 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 ...
Henry William Watson. Similarly the angle ACB is equal to the angle DFE ; there- fore the triangles 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 ...
Página 18
... Similarly the side CA must coincide with the side FD . Then , because the sides BA and CA coincide with the sides ED and FD , and because two straight lines can only intersect in one point , therefore the point A must coincide with the ...
... Similarly the side CA must coincide with the side FD . Then , because the sides BA and CA coincide with the sides ED and FD , and because two straight lines can only intersect in one point , therefore the point A must coincide with the ...
Página 22
... Similarly , CAG is equal to CGA . Therefore , BAC is equal to BGC , i.e. to EDF , and similarly for the other angles . PROPOSITION 8 . The greater angle of every triangle is subtended by the greater side , and the greater side of every ...
... Similarly , CAG is equal to CGA . Therefore , BAC is equal to BGC , i.e. to EDF , and similarly for the other angles . PROPOSITION 8 . The greater angle of every triangle is subtended by the greater side , and the greater side of every ...
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Términos y frases comunes
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
Pasajes populares
Página 15 - If two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 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.
Página 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
Página 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...
Página 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'.
Página 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.
Página 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.
Página 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