The school Euclid: comprising the first four books, by A.K. Isbister1862 |
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Side 35
... CD , make the alternate angles , AEF , EFD , equal to one another . Then AB shall be parallel to CD A E B Z F D CONSTRUCTION For , if AB be not parallel to CD , AB and CD being produced , shall meet either towards B , D , or towards A ...
... CD , make the alternate angles , AEF , EFD , equal to one another . Then AB shall be parallel to CD A E B Z F D CONSTRUCTION For , if AB be not parallel to CD , AB and CD being produced , shall meet either towards B , D , or towards A ...
Side 36
... parallel to one another . ( References - Prop . I. 13 , 15 , 27 ; ax . I. 3. ) Let the straight line EF , which falls upon the two straight lines AB , CD ... parallel to CD . E A G ' B C F DEMONSTRATION Because the angle EGB is equal to the ...
... parallel to one another . ( References - Prop . I. 13 , 15 , 27 ; ax . I. 3. ) Let the straight line EF , which falls upon the two straight lines AB , CD ... parallel to CD . E A G ' B C F DEMONSTRATION Because the angle EGB is equal to the ...
Side 37
... parallel lines AB , CD . Then the alternate angle AGĦ shall be equal to the alternate angle GHD ; and the exterior angle EGB shall be equal to the interior and opposite angle GHD , on the same side of the line EF ; and the two interior ...
... parallel lines AB , CD . Then the alternate angle AGĦ shall be equal to the alternate angle GHD ; and the exterior angle EGB shall be equal to the interior and opposite angle GHD , on the same side of the line EF ; and the two interior ...
Side 38
... parallel to the same straight line are parallel to one another . ( References - Prop . I. 27 , 29 ; ax . 1. ) Let AB , CD , be each of them parallel to EF . Then AB shall be also parallel to G A B H E F D K CONSTRUCTION Let the straight ...
... parallel to the same straight line are parallel to one another . ( References - Prop . I. 27 , 29 ; ax . 1. ) Let AB , CD , be each of them parallel to EF . Then AB shall be also parallel to G A B H E F D K CONSTRUCTION Let the straight ...
Side 42
... parallel . ( References - Prop . I. 4 , 27 , 29. ) Let AB , CD , be two equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD . Then AC , BD , shall be equal and parallel . B D CONSTRUCTION ...
... parallel . ( References - Prop . I. 4 , 27 , 29. ) Let AB , CD , be two equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD . Then AC , BD , shall be equal and parallel . B D CONSTRUCTION ...
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The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Ingen forhåndsvisning - 2009 |
Almindelige termer og sætninger
AB is equal adjacent angles alternate angles angle ABC angle AGH angle BAC angle BCD angle EAB angle EDF angle equal angles CBA base BC BC is equal circle ABC constr DEMONSTRATION describe the circle diameter double equal angles equal straight lines equal to BC equilateral and equiangular exterior angle given circle given rectilineal angle given straight line gnomon greater inscribed interior and opposite less Let ABC Let the straight opposite angles parallel to CD parallelogram pentagon perpendicular Q. E. D. PROP rectangle AE rectangle contained rectilineal figure References Prop References-Prop remaining angle required to describe right angles segment semicircle side BC square of AC straight line AB straight line AC THEOREM touches the circle triangle ABC triangle DEF twice the rectangle
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Side 141 - 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...
Side 35 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Side 71 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Side 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 61 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Side 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Side 27 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Side 77 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment.
Side 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.