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 8
... extremities of a line are points ; and the intersections " of one line with another are also points . " 3. " If two lines are such that they cannot coincide in any two points , with- " out coinciding altogether , each of them is called ...
... extremities of a line are points ; and the intersections " of one line with another are also points . " 3. " If two lines are such that they cannot coincide in any two points , with- " out coinciding altogether , each of them is called ...
Page 15
... extremity of the base equal to one another , and likewise those which are terminated in the other extremity , equal to one another . Let there be two triangles ACB , ADB , upon the same base AB , and upon the same side of it , which ...
... extremity of the base equal to one another , and likewise those which are terminated in the other extremity , equal to one another . Let there be two triangles ACB , ADB , upon the same base AB , and upon the same side of it , which ...
Page 16
... extremity equal to one another . PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other each to each , and have likewise their bases equal ; the angle which is contain ed by the two sides of the ...
... extremity equal to one another . PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other each to each , and have likewise their bases equal ; the angle which is contain ed by the two sides of the ...
Page 17
... extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ; but this is impossible ( 7. 1. ) ; therefore , if the base BC coincides with the base EF , the sides BA , AC cannot but coincide ...
... extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ; but this is impossible ( 7. 1. ) ; therefore , if the base BC coincides with the base EF , the sides BA , AC cannot but coincide ...
Page 32
... 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 ...
... 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 ...
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Common terms and phrases
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Page 12 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Page 11 - Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Page 72 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Page 84 - 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 80 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 22 - Any two sides of a triangle are together greater than the third side.
Page 53 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.