The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
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Page 7
... given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral ... point C , in which the circles cut one another , draw ( Post . 1. ) the straight lines CA , CB , to the points A , B ; ABC shall ...
... given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral ... point C , in which the circles cut one another , draw ( Post . 1. ) the straight lines CA , CB , to the points A , B ; ABC shall ...
Page 8
... given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . - PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
... given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . - PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
Page 13
... a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . Take any point Din AB , and from ACcut ( I. 3. ) off AE equal to AD ; join DE , and upon ...
... a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . Take any point Din AB , and from ACcut ( I. 3. ) off AE equal to AD ; join DE , and upon ...
Page 14
... given finite straight line , that is , to divide it into two equal parts ... point D. A. D B Because AC is equal to CB , and CD common to the two ... point D. Which was to be done . PROP . XI . - PROBLEM . To draw a straight line at right ...
... given finite straight line , that is , to divide it into two equal parts ... point D. A. D B Because AC is equal to CB , and CD common to the two ... point D. Which was to be done . PROP . XI . - PROBLEM . To draw a straight line at right ...
Page 15
Euclides Samuel A Good. straight line FC drawn from the given point C is at right angles to the given straight line AB F A D E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF , are ...
Euclides Samuel A Good. straight line FC drawn from the given point C is at right angles to the given straight line AB F A D E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF , are ...
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Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 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.
Page 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.
Page 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.
Page 7 - AB; but things which are equal to the same are equal to one another...
Page 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.
Page 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.
Page 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.
Page 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...