The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
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Side 26
... is , 4 . The angle GCB is equal to the angle DFE ; by the hypothesis , equal to the angle BCA ; wherefore also The angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; 26 EUCLID'S ELEMENTS .
... is , 4 . The angle GCB is equal to the angle DFE ; by the hypothesis , equal to the angle BCA ; wherefore also The angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; 26 EUCLID'S ELEMENTS .
Side 27
... impossible ( I. 16. ) ; wherefore BC is not unequal to EF , 5 . that is , it is equal to it ; and AB is equal ( Hyp . ) to DE ; therefore 6. The two AB , BC , are equal to the two DE , EF , each to each ; and they contain ( Hyp ...
... impossible ( I. 16. ) ; wherefore BC is not unequal to EF , 5 . that is , it is equal to it ; and AB is equal ( Hyp . ) to DE ; therefore 6. The two AB , BC , are equal to the two DE , EF , each to each ; and they contain ( Hyp ...
Side 28
... impossible ; therefore 2 . AB and CD being produced do not meet towards B , D. In like manner it may be demonstrated that 3 . AB and CD do not meet towards A , C ; but those straight lines which meet neither way , though produced ever ...
... impossible ; therefore 2 . AB and CD being produced do not meet towards B , D. In like manner it may be demonstrated that 3 . AB and CD do not meet towards A , C ; but those straight lines which meet neither way , though produced ever ...
Side 38
... impossible . Therefore 3 . AE is not parallel to BC . In the same manner , it can be demonstrated that no other line but AD is parallel to BC ; therefore 4. AD is parallel to BC . Wherefore , equal triangles upon , & c . Q.E.D. PROP ...
... impossible . Therefore 3 . AE is not parallel to BC . In the same manner , it can be demonstrated that no other line but AD is parallel to BC ; therefore 4. AD is parallel to BC . Wherefore , equal triangles upon , & c . Q.E.D. PROP ...
Side 66
... impossible ; therefore 4. G is not the centre of the circle ABC . In the same manner it can be shown , that no other point but F is the centre ; that is 5. F is the centre of the circle ABC . Which was to be found . COR . From this it ...
... impossible ; therefore 4. G is not the centre of the circle ABC . In the same manner it can be shown , that no other point but F is the centre ; that is 5. F is the centre of the circle ABC . Which was to be found . COR . From this it ...
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The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... Euclid,Samuel A. GOOD Uten tilgangsbegrensning - 1854 |
The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... Euclid,Samuel A. GOOD Uten tilgangsbegrensning - 1854 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
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 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.
Side 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.
Side 7 - AB; but things which are equal to the same are equal to one another...
Side 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.
Side 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.
Side 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.
Side 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...