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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 49
... four times the rectangle con- tained by the whole line , and one of the parts , together with the square of the other part , is equal to the square of the straight line which is made up of the whole and the first - mentioned part . Let ...
... four times the rectangle con- tained by the whole line , and one of the parts , together with the square of the other part , is equal to the square of the straight line which is made up of the whole and the first - mentioned part . Let ...
Página 50
... four rectangles AG , MP , PL , RF , are equal to one another , and so AG + MP + PL + RF = 4AG . And it was demonstrated , that CK + BN + GR + RN = 4CK ; wherefore , adding equals to equals , the whole gnomon AOH = 4AK . Now AK - AB.BK ...
... four rectangles AG , MP , PL , RF , are equal to one another , and so AG + MP + PL + RF = 4AG . And it was demonstrated , that CK + BN + GR + RN = 4CK ; wherefore , adding equals to equals , the whole gnomon AOH = 4AK . Now AK - AB.BK ...
Página 54
... four sides of the parallelogram . Let ABCD be a parallelogram , of which the diameters are AC and BD ; the sum of the squares of AC and BD is equal to the sum of the squares of AB , BC , CD , DA . A E D Let AC and BD intersect one ...
... four sides of the parallelogram . Let ABCD be a parallelogram , of which the diameters are AC and BD ; the sum of the squares of AC and BD is equal to the sum of the squares of AB , BC , CD , DA . A E D Let AC and BD intersect one ...
Página 81
... four , eight , sixteen , & c . equal parts . PROP . IV . PROB . Upon a given straight line to describe a segment of a circle , containing an angle equal to a given rectilineal angle . Let AB be the given straight line , and the angle at ...
... four , eight , sixteen , & c . equal parts . PROP . IV . PROB . Upon a given straight line to describe a segment of a circle , containing an angle equal to a given rectilineal angle . Let AB be the given straight line , and the angle at ...
Página 86
... four sides . LEMMA . Any regular polygon may be inscribed in a circle , and circumscribed about one . Let ABCDE , & c . be a regular polygon : describe a circle through the three points A , B , C , the centre being O , and OP the ...
... four sides . LEMMA . Any regular polygon may be inscribed in a circle , and circumscribed about one . Let ABCDE , & c . be a regular polygon : describe a circle through the three points A , B , C , the centre being O , and OP the ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles 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 PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore