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 |
From inside the book
Results 1-5 of 100
Page ix
... greater than the circumference of that circle , and the other less . In the same manner , the quadrature of the circle is performed only by approximation , or by finding two rectangles nearly equal to one another , one of them greater ...
... greater than the circumference of that circle , and the other less . In the same manner , the quadrature of the circle is performed only by approximation , or by finding two rectangles nearly equal to one another , one of them greater ...
Page xv
... greater than the third , neither could it be true , that the greater side of every triangle is opposite to the greater angle , nor that the equal sides are opposite to equal angles , nor , lastly , that things equal to the same thing ...
... greater than the third , neither could it be true , that the greater side of every triangle is opposite to the greater angle , nor that the equal sides are opposite to equal angles , nor , lastly , that things equal to the same thing ...
Page 21
... greater than its part . Χ . All right angles are equal to one another . XI . " Two straight lines which intersect one another , cannot be both " parallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral ...
... greater than its part . Χ . All right angles are equal to one another . XI . " Two straight lines which intersect one another , cannot be both " parallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral ...
Page 23
... greater . It is required to cut off D 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 ...
... greater . It is required to cut off D 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 ...
Page 25
... 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 , be- cause in the triangles 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 , be- cause in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC ...
Other editions - View all
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 definition demonstrated diameter draw 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 MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB 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