The Elements of Plane and Solid Geometry |
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Page ix
... follow . Hence , an inevitable confusion arises in the mind of the reader between that which is possible theoretically and con- ceivably , and that which is possible in relation to the instruments to which Euclid chooses to restrict him ...
... follow . Hence , an inevitable confusion arises in the mind of the reader between that which is possible theoretically and con- ceivably , and that which is possible in relation to the instruments to which Euclid chooses to restrict him ...
Page 9
... 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 triangle ABC to the triangle DFF ; such ...
... 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 triangle ABC to the triangle DFF ; such ...
Page 10
... follows from the first axiom and the assumption that one and only one line always exists which is shorter than any other line between two given points . The proof will stand thus : Let A and B be any two points , and 1 Geometry . ΙΟ.
... follows from the first axiom and the assumption that one and only one line always exists which is shorter than any other line between two given points . The proof will stand thus : Let A and B be any two points , and 1 Geometry . ΙΟ.
Page 16
... follows : Suppose the page upon which the Figs . 6 , 7 , and 8 are drawn to be coloured red , and the back of the page to be coloured green . Let the triangle ABC be cut out of the sheet of paper . Then the triangle ABC so cut out may ...
... follows : Suppose the page upon which the Figs . 6 , 7 , and 8 are drawn to be coloured red , and the back of the page to be coloured green . Let the triangle ABC be cut out of the sheet of paper . Then the triangle ABC so cut out may ...
Page 20
... follows : Fig . 21 . A B D C Let ABC be an isosceles triangle having the sides AB and AC equal , then shall the angles ABC and ACB be also equal . Let D be the middle point of BC and join AD . Then the three sides of the triangle ABD ...
... follows : Fig . 21 . A B D C Let ABC be an isosceles triangle having the sides AB and AC equal , then shall the angles ABC and ACB be also equal . Let D be the middle point of BC and join AD . Then the three sides of the triangle ABD ...
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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