Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., EnlJ.B. Lippincott & Company, 1866 - 317 Seiten |
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Seite 17
... construction , each of the halves BAF , CAF , may be divi ded into two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . X. PROB ...
... construction , each of the halves BAF , CAF , may be divi ded into two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . X. PROB ...
Seite 37
... construction will apply to the problem : to make a triangle equivalent to a given rectangle . PROP . XLIII . THEOR . The complements of the parallelograms which are about the diameter of any parallelogram , are equal to one another ...
... construction will apply to the problem : to make a triangle equivalent to a given rectangle . PROP . XLIII . THEOR . The complements of the parallelograms which are about the diameter of any parallelogram , are equal to one another ...
Seite 45
... construction will apply : for , mak ing BCA equal to the given angle , and AC equal to the adjacent side ; then , from A as centre , with a radius equal to the other given side , describe an arc , cutting CB in B ; draw AB , and CAB ...
... construction will apply : for , mak ing BCA equal to the given angle , and AC equal to the adjacent side ; then , from A as centre , with a radius equal to the other given side , describe an arc , cutting CB in B ; draw AB , and CAB ...
Seite 46
... construction which reduces two of them to one , will reduce three of them to two , and these two to one , and so of others . PROP . I. PROB . To find the side of a square equivalent to the difference of two given squares . Draw , as in ...
... construction which reduces two of them to one , will reduce three of them to two , and these two to one , and so of others . PROP . I. PROB . To find the side of a square equivalent to the difference of two given squares . Draw , as in ...
Seite 64
... construction being made , because the radii EA , FB are equal to one another , the angle EAF is equal ( 5. 1. ) to the angle EBF ; and the right angle AFE is equal to the right angle BFE : Therefore , in the two triangles EAF , EBF ...
... construction being made , because the radii EA , FB are equal to one another , the angle EAF is equal ( 5. 1. ) to the angle EBF ; and the right angle AFE is equal to the right angle BFE : Therefore , in the two triangles EAF , EBF ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described 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 proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore