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 17
... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given ... ABC , and bisect ( 9. 1. ) the angle ACB by the straight line CD . AB is cut into two equal parts in the point D ...
... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given ... ABC , and bisect ( 9. 1. ) the angle ACB by the straight line CD . AB is cut into two equal parts in the point D ...
Page 19
... angle CBA be equal to ABD , each of them is a right angle ( Def . 7. ) ; but , if not , from the point B draw BE at right angles ( 11. 1. ) E A D B D B to CD ; therefore ... angles ABC , ABE are together equal OF GEOMETRY . BOOK I. 19.
... angle CBA be equal to ABD , each of them is a right angle ( Def . 7. ) ; but , if not , from the point B draw BE at right angles ( 11. 1. ) E A D B D B to CD ; therefore ... angles ABC , ABE are together equal OF GEOMETRY . BOOK I. 19.
Page 20
... ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax . ) to the remaining angle ...
... ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax . ) to the remaining angle ...
Page 21
... angle ACD , is greater than the B OF GEOMETRY . BOOK I. 21 F. 4. C D angle ABC . G. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are ...
... angle ACD , is greater than the B OF GEOMETRY . BOOK I. 21 F. 4. C D angle ABC . G. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are ...
Page 22
... angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB . For ...
... angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB . For ...
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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 demonstrated 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 multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP 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 third 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 149 - IF an angle of a triangle be bisected by a straight line, which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of...
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 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
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, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
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 296 - 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 50 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Page 15 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Page 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...