The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
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Αποτελέσματα 6 - 10 από τα 41.
Σελίδα 23
... point F is the centre of the circle DKL , ( Def . 15. ) 1. FD is equal to FK ; but FD is equal to the straight line ; therefore 2. FK is equal to △ . Again , because G is the centre of the circle BOOK I. - PROP , XXI . XXII . 23.
... point F is the centre of the circle DKL , ( Def . 15. ) 1. FD is equal to FK ; but FD is equal to the straight line ; therefore 2. FK is equal to △ . Again , because G is the centre of the circle BOOK I. - PROP , XXI . XXII . 23.
Σελίδα 31
... point 4 , in the straight line AD , make ( I. 23. ) the angle DAE equal to the angle ADC ; and produce the straight line EA to F ; EF is parallel to BC . E F B D Because the straight line AD , which meets the two straight lines BC , EF ...
... point 4 , in the straight line AD , make ( I. 23. ) the angle DAE equal to the angle ADC ; and produce the straight line EA to F ; EF is parallel to BC . E F B D Because the straight line AD , which meets the two straight lines BC , EF ...
Σελίδα 32
... point F within the figure to each of its angles . And by the preceding proposition , ali the angles of these triangles are equal to twice as many right angles as there are triangles , that is , as there are sides of the figure ; and the ...
... point F within the figure to each of its angles . And by the preceding proposition , ali the angles of these triangles are equal to twice as many right angles as there are triangles , that is , as there are sides of the figure ; and the ...
Σελίδα 37
... points G , H , and through B draw BG parallel ( I. 31. ) to CA , and through F draw FH parallel to ED . Then ( I. 34. Def . ) 1 . and ( I. 36. ) Each of the figures GBCA , DEFH , is a parallelogram ; 2. GBCA , DEFH , are equal to one ...
... points G , H , and through B draw BG parallel ( I. 31. ) to CA , and through F draw FH parallel to ED . Then ( I. 34. Def . ) 1 . and ( I. 36. ) Each of the figures GBCA , DEFH , is a parallelogram ; 2. GBCA , DEFH , are equal to one ...
Σελίδα 49
... point C ; the rectangle AB , BC , is equal to the rectangle AC , CB , together with the square of BC . C F D E Upon BC describe ( I. 46. ) the square CDEB , and produce ED to F ; and through draw ( I. 31. ) AF parallel to CD or BE ...
... point C ; the rectangle AB , BC , is equal to the rectangle AC , CB , together with the square of BC . C F D E Upon BC describe ( I. 46. ) the square CDEB , and produce ED to F ; and through draw ( I. 31. ) AF parallel to CD or BE ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal adjacent angles AF is equal angle ABC angle ACB angle AGH angle BAC angle BCD angle DEF angle EAB angle EDF angle equal base BC bisected circle ABC cuts the circle describe a circle diameter double equal angles equal Constr equal Hyp equal straight lines equal to BC equiangular equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given rectilineal angle given straight line given triangle gnomon greater inscribed join Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F Q.E.D. PROP rectangle AD rectangle AE rectangle contained rectilineal figure remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC touches the circle triangle ABC triangle DEF twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 26 - 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...
Σελίδα 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 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.
Σελίδα 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Σελίδα 97 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - AB; but things which are equal to the same are equal to one another...
Σελίδα 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Σελίδα 53 - 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.
Σελίδα 41 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 52 - 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...