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 11 - 15 από τα 34.
Σελίδα 28
... alternate angles equal to one another , these two straight lines shall be parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD , equal to one another ; AB is ...
... alternate angles equal to one another , these two straight lines shall be parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD , equal to one another ; AB is ...
Σελίδα 29
... angles BGH , GHD . Take away the common angle BGH ; therefore 2 . The remaining angle AGH is equal to the remaining angle GHD , and they are alternate angles ; therefore ( I. 27. ) 3. AB is parallel to CD . Wherefore if a straight line ...
... angles BGH , GHD . Take away the common angle BGH ; therefore 2 . The remaining angle AGH is equal to the remaining angle GHD , and they are alternate angles ; therefore ( I. 27. ) 3. AB is parallel to CD . Wherefore if a straight line ...
Σελίδα 31
... angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . Let ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is ...
... angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . Let ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is ...
Σελίδα 33
... angles to the other angles , each to each , to which the equal sides are opposite ; therefore 3. The angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC , BD , and makes the alternate ...
... angles to the other angles , each to each , to which the equal sides are opposite ; therefore 3. The angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC , BD , and makes the alternate ...
Σελίδα 34
... alternate angles ABC , BCD , are equal to one another ; and because AC is parallel to BD , and BC meets them , ( 1. 29. ) 2. The alternate angles ACB , CBD , are equal to one another ; wherefore the two triangles ABC , CBD , have two angles ...
... alternate angles ABC , BCD , are equal to one another ; and because AC is parallel to BD , and BC meets them , ( 1. 29. ) 2. The alternate angles ACB , CBD , are equal to one another ; wherefore the two triangles ABC , CBD , have two angles ...
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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...