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 7
... AC is equal to AB ; and because the point B is the centre of the circle ACE , 2. BC is equal to BA . But it has been proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB ; but things which are equal to the same ...
... AC is equal to AB ; and because the point B is the centre of the circle ACE , 2. BC is equal to BA . But it has been proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB ; but things which are equal to the same ...
Side 9
... equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF : the base BC shall be equal ...
... equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and the angle BAC equal to the angle EDF : the base BC shall be equal ...
Side 10
... equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABCbe an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC , be ...
... equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABCbe an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC , be ...
Side 11
... equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC ...
... equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC ...
Side 12
... AC is equal to AD , ( I. 5. ) 1. The angle ACD is equal to the angle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ; therefore also 2 . The angle ADC is greater than BCD ; much more then 3. The angle BDC is ...
... AC is equal to AD , ( I. 5. ) 1. The angle ACD is equal to the angle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ; therefore also 2 . The angle ADC is greater than BCD ; much more then 3. The angle BDC is ...
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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
AC is equal adjacent angles AF is equal angle ABC angle ACB angle AGH angle BAC angle BCD angle DEF angle EDF angle equal base BC bisected circle ABC cuts the circle describe a circle diameter double draw 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 THEOREM 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...