Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical Trigonometry |
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Page 61
... radius of a circle is the straight line drawn from the centre to the circumference . THE I. A straight line is said to touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are said to touch one ...
... radius of a circle is the straight line drawn from the centre to the circumference . THE I. A straight line is said to touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are said to touch one ...
Page 97
... radius of the given circle , so that the rectangle con- tained by the whole and one of the parts may be equal to the square of the other ( 11. 2. ) . Apply in the circle , on each side of a given point , a line equal to the greater of ...
... radius of the given circle , so that the rectangle con- tained by the whole and one of the parts may be equal to the square of the other ( 11. 2. ) . Apply in the circle , on each side of a given point , a line equal to the greater of ...
Page 101
... radius of the circle . And if through the points A , B , C , D. E , F , there be drawn straight lines touching the circle , an equilateral and equiangular hexagon shall be described about it , which may be demonstrated from what has ...
... radius of the circle . And if through the points A , B , C , D. E , F , there be drawn straight lines touching the circle , an equilateral and equiangular hexagon shall be described about it , which may be demonstrated from what has ...
Page 150
... radius : and if from these points two straight lines be drawn to any point whatsoever in the circumfer- ence of the circle , the ratio of these lines will be the same with the ratio of the segments intercepted between the two first ...
... radius : and if from these points two straight lines be drawn to any point whatsoever in the circumfer- ence of the circle , the ratio of these lines will be the same with the ratio of the segments intercepted between the two first ...
Page 153
... radius AC , the greater of the two -sides , describe the circle CFG : produce AB to meet the circumfer- ence in E and F , and CB to meet it in G. Then because AF - AC , BF AB + AC , the sum of the sides ; and since AE = AC , BE = AC ...
... radius AC , the greater of the two -sides , describe the circle CFG : produce AB to meet the circumfer- ence in E and F , and CB to meet it in G. Then because AF - AC , BF AB + AC , the sum of the sides ; and since AE = AC , BE = AC ...
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Common terms and phrases
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC meet multiple opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Page 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Page 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.
Page 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Page 30 - If, from the ends of the 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 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Page 51 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Page 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.