The Elements of Plane and Solid GeometryLongmans, Green, and Company, 1872 - 285 sider |
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Resultat 1-5 av 31
Side xiii
... 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 ...
Side 4
... . A C B A D * This axiom may be otherwise stated as follows : - D If two straight lines have more than one point in common they lie in one and the same straight line . Thus in figure 1 , the lines ACB and ADB 4 Geometry .
... . A C B A D * This axiom may be otherwise stated as follows : - D If two straight lines have more than one point in common they lie in one and the same straight line . Thus in figure 1 , the lines ACB and ADB 4 Geometry .
Side 9
... follow that the portion of superficial space ABC was , as to shape and size , exactly identical with . the portion DEF . A B E C D In such a case as this we often speak of transferring the triangle ABC to the triangle DEF ; such ...
... follow that the portion of superficial space ABC was , as to shape and size , exactly identical with . the portion DEF . A B E C D In such a case as this we often speak of transferring the triangle ABC to the triangle DEF ; such ...
Side 10
... statement , but that it 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 ΙΟ Geometry . BOOK II.
... statement , but that it 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 ΙΟ Geometry . BOOK II.
Side 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 ...
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ABC and DEF ABCD AC is equal adjacent angles angle ABC angle BAC antecedent area of AC bisects the angle centre chords circumference coincide common measure containing Corollary 2.-If DEFINITION diameter dicular dihedral angle distance divided equal angles equal in area equal to AB equal to AC exterior angle finite straight line given angle given circle given plane given point given ratio given straight line greater homologous incommensurable inscribed length less Let ABC line joining locus middle point multiple number of sides numerator and denominator opposite sides parallelogram pentagon perpen perpendicular plane AC point F produced Prop PROPOSITION PROPOSITION 14 proved radius ratio be equal rectangle regular polygon respectively equal right angles segments Similarly situated square straight line AB straight line BC subtended tangent triangle ABC triangle DEF
Populære avsnitt
Side 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.
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Side 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.
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Side 19 - If two triangles have two sides of the one equal to two sides of the other, each to each, and" have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them, of the other.
Side 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
Side 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...
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Side 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'.
Side 30 - Any two angles of a triangle are together less than two right angles.