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 20
... square is that which has all its sides equal , and all its angles right angles . XXVI . An oblong , is that which has all its angles right angles , but has not all its sides equal . XXVII . A rhombus , is that which has all its sides ...
... square is that which has all its sides equal , and all its angles right angles . XXVI . An oblong , is that which has all its angles right angles , but has not all its sides equal . XXVII . A rhombus , is that which has all its sides ...
Page 50
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( 11. 1. ) AC at right angles to AB ; and make ( 3. 1. ) AD equal to AB , and through the ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( 11. 1. ) AC at right angles to AB ; and make ( 3. 1. ) AD equal to AB , and through the ...
Page 51
... square described upon the side BC is equal to the squares de- scribed upon BA , AC . On BC describe ( 46. 1. ) the square BDEC , and on BA , AC the squares GB , HC ; and through A draw ( 31. 1. ) AL parallel to BD or CE , and join AD ...
... square described upon the side BC is equal to the squares de- scribed upon BA , AC . On BC describe ( 46. 1. ) the square BDEC , and on BA , AC the squares GB , HC ; and through A draw ( 31. 1. ) AL parallel to BD or CE , and join AD ...
Page 52
... square GB : And , in the same man- ner , by joining AE , BK , it is demonstrated that the parallelogram CL is equal to the square HC . Therefore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is de ...
... square GB : And , in the same man- ner , by joining AE , BK , it is demonstrated that the parallelogram CL is equal to the square HC . Therefore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is de ...
Page 53
... square of a line , for " instance of AD , we shall frequently in what follows write AD2 . " " The sign + placed between the names of two magnitudes , signi- " fies that those magnitudes are to be added together : and the sign " -placed ...
... square of a line , for " instance of AD , we shall frequently in what follows write AD2 . " " The sign + placed between the names of two magnitudes , signi- " fies that those magnitudes are to be added together : and the sign " -placed ...
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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.