The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 8
... Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . II ...
... Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . II ...
Página 26
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced shall meet ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced shall meet ...
Página 27
... parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . Ir a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the ...
... parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . Ir a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the ...
Página 28
... parallel to one another . Let AB , CD , be each of them parallel to EF , AB is also parallel to CD . A G B Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight lines AB , EF , the angle AGH is equal ...
... parallel to one another . Let AB , CD , be each of them parallel to EF , AB is also parallel to CD . A G B Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight lines AB , EF , the angle AGH is equal ...
Página 29
... parallel ( 31. 1. ) to the straight line AB ; and because AB is parallel to CE and AC meets them , the alternate an- gles BAC , ACE are equal ( 29 . 1. ) Again ; because A is pa- rallel to CE , and BD falls upon them , the exterior ...
... parallel ( 31. 1. ) to the straight line AB ; and because AB is parallel to CE and AC meets them , the alternate an- gles BAC , ACE are equal ( 29 . 1. ) Again ; because A is pa- rallel to CE , and BD falls upon them , the exterior ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 36 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Página 145 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 65 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 248 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Página 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 121 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 21 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 14 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Página 80 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.