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 16 - 20 από τα 34.
Σελίδα 42
... angles FKH , GHM , 1. The angle FKH is equal to GHM ; add to each of these the angle KHG ; therefore 2. The angles ... opposite sides of it , make the adjacent angles equal to two right angles , ( I.14 . ) 4. KH is in the same straight ...
... angles FKH , GHM , 1. The angle FKH is equal to GHM ; add to each of these the angle KHG ; therefore 2. The angles ... opposite sides of it , make the adjacent angles equal to two right angles , ( I.14 . ) 4. KH is in the same straight ...
Σελίδα 44
... opposite angles of parallelograms are equal ( I. 34. ) ; therefore 6. Each of the opposite angles ABE , BED , is a right angle ; wherefore 7. The figure ADEB is rectangular , and it has been demonstrated that it is equilateral ...
... opposite angles of parallelograms are equal ( I. 34. ) ; therefore 6. Each of the opposite angles ABE , BED , is a right angle ; wherefore 7. The figure ADEB is rectangular , and it has been demonstrated that it is equilateral ...
Σελίδα 47
... opposite angles of the parallelograms which make the gnomon . " PROP . I. - THEOREM . If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the two straight lines , is equal to ...
... opposite angles of the parallelograms which make the gnomon . " PROP . I. - THEOREM . If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the two straight lines , is equal to ...
Σελίδα 50
... opposite angle ADB ; but ( I. 5. ) 2 . ADB is equal to the angle ABD , because BA is equal to AD , being sides of a ... angles KBC , GCB , are equal to two right angles ; and KBC is ( Def . 30. ) a right angle ; wherefore 7. GCB is a ...
... opposite angle ADB ; but ( I. 5. ) 2 . ADB is equal to the angle ABD , because BA is equal to AD , being sides of a ... angles KBC , GCB , are equal to two right angles ; and KBC is ( Def . 30. ) a right angle ; wherefore 7. GCB is a ...
Σελίδα 56
... angles to AB , and make it equal ( I. 3. ) to 4C or CB , and join EA , EB ... opposite angle ECB , the re- maining angle EFG is half a right angle ... opposite angle ECB , the remaining angle BFD is half a right angle ; therefore 7. The ...
... angles to AB , and make it equal ( I. 3. ) to 4C or CB , and join EA , EB ... opposite angle ECB , the re- maining angle EFG is half a right angle ... opposite angle ECB , the remaining angle BFD is half a right angle ; therefore 7. The ...
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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...