The Elements of Euclid with Many Additional Propositions and Explanatory NotesJ. Weale, 1860 |
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Resultat 1-5 av 71
Side 10
... fore the lines BC and AL , being both equal to the same line BG , are equal to each other ( h ) . Therefore , from a given point A , a straight line has been drawn equal to a given straight line BC . SCHOLIA . 1. The construction of ...
... fore the lines BC and AL , being both equal to the same line BG , are equal to each other ( h ) . Therefore , from a given point A , a straight line has been drawn equal to a given straight line BC . SCHOLIA . 1. The construction of ...
Side 16
... fore the angle DAF is equal to the angle EAF ( d ) , and the given rectilineal angle BAC is bisected by the straight line AF . B / ( a ) I. 3 . ( b ) I. 1 . ( c ) Solution . ( d ) I. 8 . SCHOLIA . 1. The direction to construct the ...
... fore the angle DAF is equal to the angle EAF ( d ) , and the given rectilineal angle BAC is bisected by the straight line AF . B / ( a ) I. 3 . ( b ) I. 1 . ( c ) Solution . ( d ) I. 8 . SCHOLIA . 1. The direction to construct the ...
Side 22
... fore the angles ADB and ABD are equal ( c ) . But the angle ADB , being the external angle of the triangle BCD , is greater than the internal opposite angle C ( d ) , therefore the angle ABD is greater than the angle C ; and as ABC is ...
... fore the angles ADB and ABD are equal ( c ) . But the angle ADB , being the external angle of the triangle BCD , is greater than the internal opposite angle C ( d ) , therefore the angle ABD is greater than the angle C ; and as ABC is ...
Side 29
... fore the angle CAB is equal to the angle DAB , and the side CB to BD ( b ) ; and therefore the base CD is bisected , and also the angle CAD opposite to the base . B ( a ) Hypoth . ( b ) I. 26 . COROLLARY 2. It is evident that a straight ...
... fore the angle CAB is equal to the angle DAB , and the side CB to BD ( b ) ; and therefore the base CD is bisected , and also the angle CAD opposite to the base . B ( a ) Hypoth . ( b ) I. 26 . COROLLARY 2. It is evident that a straight ...
Side 30
... fore the lines AB and CD do not meet on the side BD , and in like manner it can be proved that they do not meet on the side AC . Since , then , the lines AB and CD , when produced on either side , do not meet , they are parallel ( c ) ...
... fore the lines AB and CD do not meet on the side BD , and in like manner it can be proved that they do not meet on the side AC . Since , then , the lines AB and CD , when produced on either side , do not meet , they are parallel ( c ) ...
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Vanlige uttrykk og setninger
AC is equal altitude angle ABC bisected circle ABCD circumference cone CONSTRUCTION contained COROLLARY cylinder DEMONSTRATION diameter divided double draw duplicate ratio EFGH equal angles equal in area equiangular equilateral equimultiples Euclid external angle fore fourth given line given rectilineal given straight line gnomon greater ratio homologous sides Hypoth HYPOTHESES inscribed join less line AC lines be drawn meet multiple opposite angle parallel parallelogram perpendicular polygon prism proposition pyramid ABCG pyramid DEFH rectangle rectilineal figure remaining angle right angles SCHOLIA SCHOLIUM segment side AC solid angle solid CD solid parallelopipeds sphere square on AB square on AC syllogism THEOREM THEOREM.-If third three plane angles tiple triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 107 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Side 85 - ... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another.
Side 18 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding...
Side 82 - From the point A draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the triangle ABC, viz. to BC ; as CD is to DA, so is (2.
Side 111 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 116 - ... plane, from a given point above it. Let A be the given point above the plane BH; it is required to draw from the point A a straight line perpendicular to the plane BH.
Side 115 - For the same reason, CD is likewise at right angles to the plane HGK. Therefore AB, CD are each of them at right angles to the plane HGK.
Side 49 - IF magnitudes, taken jointly, be proportionals, they shall also be proportionals when taken separately ; that is, if two magnitudes together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same ratio which the remaining one of the last two has to the other of these. Let AB, BE, CD...
Side 32 - 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.
Side 34 - Take of B and D any equimultiples whatever E and F; and of A and C any equimultiples whatever G and H. First, let E be greater than G, then G is less than E: and because A is to B, as C is to D, (hyp.) and of A and C...