The school Euclid: comprising the first four books, by A.K. Isbister1862 |
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Página 46
... ( 1. 35 ) and because the diameter AB bisects the parallelogram EBCA ; therefore the triangle ABC is the half of EBCA ; ( 1. 34 ) and because the diameter DC bisects the parallelogram DBCF , 46 [ BOOK I. THE SCHOOL EUCLID .
... ( 1. 35 ) and because the diameter AB bisects the parallelogram EBCA ; therefore the triangle ABC is the half of EBCA ; ( 1. 34 ) and because the diameter DC bisects the parallelogram DBCF , 46 [ BOOK I. THE SCHOOL EUCLID .
Página 47
... half of GBCA ; ( 1. 34 ) and because the diameter DF bisects the parallelogram DEFH , therefore the triangle DEF is the half of DEFH ; 6 but things which are halves of the same are equal to one another , ' ( ax 7. ) therefore the ...
... half of GBCA ; ( 1. 34 ) and because the diameter DF bisects the parallelogram DEFH , therefore the triangle DEF is the half of DEFH ; 6 but things which are halves of the same are equal to one another , ' ( ax 7. ) therefore the ...
Página 64
... half the line . ( References - Prop . I. 31 , 34 , 36 , 43 , 46 ; II . 4 , Cor . ) Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D. Then the rectangle AD , DB ...
... half the line . ( References - Prop . I. 31 , 34 , 36 , 43 , 46 ; II . 4 , Cor . ) Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts at the point D. Then the rectangle AD , DB ...
Página 65
... half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced . ( References - Prop . I. 31 , 36 , 43 ; II . 4 , Cor . ) Let the straight line AB be bisected in C , and produced ...
... half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced . ( References - Prop . I. 31 , 36 , 43 ; II . 4 , Cor . ) Let the straight line AB be bisected in C , and produced ...
Página 69
... half the line , and of the square of the line between the points of section . ( Reference - Prop . r . 3 , 5 , 6 , 11 , 29 , 31 , 32 , 34 , 47. ) Let the straight line AB be divided into two equal parts in the point C , and into unequal ...
... half the line , and of the square of the line between the points of section . ( Reference - Prop . r . 3 , 5 , 6 , 11 , 29 , 31 , 32 , 34 , 47. ) Let the straight line AB be divided into two equal parts in the point C , and into unequal ...
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The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Sin vista previa disponible - 2009 |
Términos y frases comunes
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
Pasajes populares
Página 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...
Página 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.
Página 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...
Página 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.
Página 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...
Página 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Página 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.
Página 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.
Página 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.