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 70
Euclides Samuel A Good. Let the two circles ABC , CDE , touch one another internally in the point C ; they have not ... circle ABC , ( I. Def . 15. ) 1. CF is equal to FB ; also , because F is the centre of the circle CDE , 2 . CF is ...
Euclides Samuel A Good. Let the two circles ABC , CDE , touch one another internally in the point C ; they have not ... circle ABC , ( I. Def . 15. ) 1. CF is equal to FB ; also , because F is the centre of the circle CDE , 2 . CF is ...
Side 71
... circle , and straight lines be drawn from it to the circumference , whereof one passes through the centre ; of those ... ABC be a circle , and D any point BOOK III . - PROP . VII . VIII . 71.
... circle , and straight lines be drawn from it to the circumference , whereof one passes through the centre ; of those ... ABC be a circle , and D any point BOOK III . - PROP . VII . VIII . 71.
Side 72
... circumference HLKG , the least is DG between the point D and the diameter AG ; and the nearer to it is always less than the more remote , viz . DK than DL , and DL than DH . N H M KI A Take ( III . 1. ) M the centre of the circle ABC ...
... circumference HLKG , the least is DG between the point D and the diameter AG ; and the nearer to it is always less than the more remote , viz . DK than DL , and DL than DH . N H M KI A Take ( III . 1. ) M the centre of the circle ABC ...
Side 73
... circle , from which there fall more than two equal straight lines to the circumference , that point is the centre of the circle . Let the point D be taken within the circle ABC , from which to the circumference there fall more than two ...
... circle , from which there fall more than two equal straight lines to the circumference , that point is the centre of the circle . Let the point D be taken within the circle ABC , from which to the circumference there fall more than two ...
Side 74
... circle ABC . Wherefore if a point be taken , & c . Q.E.D. PROP . X. - THEOREM . One circumference of a circle cannot cut another in more than two points . If it be possible , let the circumference FAB cut the circumference DEF in more ...
... circle ABC . Wherefore if a point be taken , & c . Q.E.D. PROP . X. - THEOREM . One circumference of a circle cannot cut another in more than two points . If it be possible , let the circumference FAB cut the circumference DEF in more ...
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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...