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 13
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
Page 14
... greater cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . 1 B A Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the ...
... greater cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . 1 B A Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the ...
Page 15
... greater than the other : Let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the less , and join DC ; therefore , because in the tri- angles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC ...
... greater than the other : Let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the less , and join DC ; therefore , because in the tri- angles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC ...
Page 16
... greater than it ; which is impossi ble . E F But if one of the vertices , as D , be within the other triangle ACB ... greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC ...
... greater than it ; which is impossi ble . E F But if one of the vertices , as D , be within the other triangle ACB ... greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC ...
Page 20
... greater , which is im- possible ; therefore BE is not in the same straight line with BC . And in like manner , it ... greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to ...
... greater , which is im- possible ; therefore BE is not in the same straight line with BC . And in like manner , it ... greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to ...
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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.