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 86
... arch ; it is required to bisect it . Join AB , and bisect ( 10. 1. ) it in C ; from the point C draw CD at right angles to AB , and join AD , DB : the arch ADB is bisected in the point D. Because AC ... AC , CD are equal to D the two BC ...
... arch ; it is required to bisect it . Join AB , and bisect ( 10. 1. ) it in C ; from the point C draw CD at right angles to AB , and join AD , DB : the arch ADB is bisected in the point D. Because AC ... AC , CD are equal to D the two BC ...
Page 101
... arches , therefore the arch BD " is one - tenth of the circumference ; and the straight line BD , that is " AC , is therefore equal to the side of an equilateral decagon inscrib- " ed in the circle BDE . " PROP . XI . PROB . To inscribe ...
... arches , therefore the arch BD " is one - tenth of the circumference ; and the straight line BD , that is " AC , is therefore equal to the side of an equilateral decagon inscrib- " ed in the circle BDE . " PROP . XI . PROB . To inscribe ...
Page 106
... AC be the side of an equilateral triangle inscribed ( 2. 4. ) in the circle , and AB the side of an equi- lateral ... arch ABC , being the third part of the whole , contains five ; and the arch AB , which is the fifth part of the ...
... AC be the side of an equilateral triangle inscribed ( 2. 4. ) in the circle , and AB the side of an equi- lateral ... arch ABC , being the third part of the whole , contains five ; and the arch AB , which is the fifth part of the ...
Page 151
... AC meets them , the alternate angles BAC , ACD are equal ( 29. 1. ) ; for the same reason , the angle CDE is equal ... arch BC to the arch EF , so is the angle BGC to the angle EHF , and the angle BAC to the angle EDF and also the ...
... AC meets them , the alternate angles BAC , ACD are equal ( 29. 1. ) ; for the same reason , the angle CDE is equal ... arch BC to the arch EF , so is the angle BGC to the angle EHF , and the angle BAC to the angle EDF and also the ...
Page 153
... arch BL be equal to EN , the sector BGL is equal to the sector EHN ; A D L G H N K B M E XC F and if the arch BL be ... AC is equal to the rectangle BD.DC , together with the square of AD . Describe the circle ( 5. 4. ) ACB about ...
... arch BL be equal to EN , the sector BGL is equal to the sector EHN ; A D L G H N K B M E XC F and if the arch BL be ... AC is equal to the rectangle BD.DC , together with the square of AD . Describe the circle ( 5. 4. ) ACB about ...
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Common terms and phrases
ABC is equal ABCD 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 magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 56 - 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 19 - 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 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Page 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Page 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Page 130 - 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 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...
Page 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Page 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Page 55 - 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.