The school Euclid: comprising the first four books, by A.K. Isbister1862 |
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Seite 8
... a part equal to C , the less . D B E CONSTRUCTION From the point A draw the straight line AD equal to C ; ( 1.2 ) and from the ... BAC equal to the angle EDF . Then the base BC shall be equal to the base 8 [ BOOK I. THE SCHOOL EUCLID .
... a part equal to C , the less . D B E CONSTRUCTION From the point A draw the straight line AD equal to C ; ( 1.2 ) and from the ... BAC equal to the angle EDF . Then the base BC shall be equal to the base 8 [ BOOK I. THE SCHOOL EUCLID .
Seite 9
... angle BAC being equal to the angle EDF , ( hyp . ) therefore AC shall coincide with DF ; and because AC is equal to DF , wherefore also the point C shall coincide with the point F. But the point B coincides with the point E ; wherefore ...
... angle BAC being equal to the angle EDF , ( hyp . ) therefore AC shall coincide with DF ; and because AC is equal to DF , wherefore also the point C shall coincide with the point F. But the point B coincides with the point E ; wherefore ...
Seite 14
Euclides Alexander Kennedy Isbister. but the angle ECD is greater than the angle BCD ; ( ax . 9 ) wherefore the angle ... BAC shall be equal to the angle EDF . A Δ Δ B F DEMONSTRATION For , if the triangle ABC be applied to 14 [ BOOK I ...
Euclides Alexander Kennedy Isbister. but the angle ECD is greater than the angle BCD ; ( ax . 9 ) wherefore the angle ... BAC shall be equal to the angle EDF . A Δ Δ B F DEMONSTRATION For , if the triangle ABC be applied to 14 [ BOOK I ...
Seite 15
... angle BAC coincides with the angle EDF , and is equal to it . ( ax . 8. ) Therefore , if two triangles , & c . Q. E. D. PROP . IX.- PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles ...
... angle BAC coincides with the angle EDF , and is equal to it . ( ax . 8. ) Therefore , if two triangles , & c . Q. E. D. PROP . IX.- PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles ...
Seite 16
... angle DAF is equal to the angle EAF . ( 1. 8. ) Wherefore the given rectilineal angle BAC is bisected by the line AF . Q. E. F PROP . X.- PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts ...
... angle DAF is equal to the angle EAF . ( 1. 8. ) Wherefore the given rectilineal angle BAC is bisected by the line AF . Q. E. F PROP . X.- PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts ...
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The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Keine Leseprobe verfügbar - 2009 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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...
Seite 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.
Seite 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...
Seite 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.
Seite 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...
Seite 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Seite 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.
Seite 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.
Seite 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.