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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 22
... triangle upon a given finite straight line Let AB be the given straight line ; it is required to describe an equilateral triangle ... ABC is an equilateral triangle . D A B E Because the point A is the centre of the circle BCD , AC is equal ( ...
... triangle upon a given finite straight line Let AB be the given straight line ; it is required to describe an equilateral triangle ... ABC is an equilateral triangle . D A B E Because the point A is the centre of the circle BCD , AC is equal ( ...
Σελίδα 23
... Geometry of Solids ; to which are Added Elements of Plane and Spherical ... ABC , DEF be two triangles which have the two sides AB , AC equal to the two ... triangle ABC to the tri- angle DEF ; and the D other angles , to which B E F ...
... Geometry of Solids ; to which are Added Elements of Plane and Spherical ... ABC , DEF be two triangles which have the two sides AB , AC equal to the two ... triangle ABC to the tri- angle DEF ; and the D other angles , to which B E F ...
Σελίδα 24
... triangle ABC be applied to the triangle DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide ...
... triangle ABC be applied to the triangle DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall coincide ...
Σελίδα 25
... ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the triangle ABC : And it ... triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides ...
... ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the triangle ABC : And it ... triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides ...
Σελίδα 26
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ... ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB ...
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ... ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB ...
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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 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 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