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 63
... difference between the other two . Hence , the trian- gle is impossible when the distance between the centres is less than the difference of the radii ; and consequently the two circles cannot cut each other . PROP . XI . THEOR . If two ...
... difference between the other two . Hence , the trian- gle is impossible when the distance between the centres is less than the difference of the radii ; and consequently the two circles cannot cut each other . PROP . XI . THEOR . If two ...
Página 64
... difference of the radii , the two circles will touch each other inter- nally . PROP . XII . THEOR . If two circles touch each other externally , the straight line which joins their centres will pass through the point of contact . Let ...
... difference of the radii , the two circles will touch each other inter- nally . PROP . XII . THEOR . If two circles touch each other externally , the straight line which joins their centres will pass through the point of contact . Let ...
Página 98
... and the arc AB , which is the fifth part of the whole , contains three ; therefore BC their difference contains two of the same parts : bisect ( Prob . 3. 3. ) BC B E D in E ; therefore BE , EC are , each 98 ELEMENTS.
... and the arc AB , which is the fifth part of the whole , contains three ; therefore BC their difference contains two of the same parts : bisect ( Prob . 3. 3. ) BC B E D in E ; therefore BE , EC are , each 98 ELEMENTS.
Página 105
... difference of the numbers is of unity . Let mA and nA be multiples of the magnitude A , by the numbers m and n , and let m be greater than n ; mA — nĂ contains A as oft as m - n con- tains unity , or mà — nA = ( m - n ) A . Let m - n ...
... difference of the numbers is of unity . Let mA and nA be multiples of the magnitude A , by the numbers m and n , and let m be greater than n ; mA — nĂ contains A as oft as m - n con- tains unity , or mà — nA = ( m - n ) A . Let m - n ...
Página 106
... difference of the two numbers is equal to unity or m— a = 1 , then mA — nA = A . PROP . A. THEOR . If four magnitudes be proportionals , they are proportionals also when taken inversely . If A B C D , then also B : A :: D : C. Let mA ...
... difference of the two numbers is equal to unity or m— a = 1 , then mA — nA = A . PROP . A. THEOR . If four magnitudes be proportionals , they are proportionals also when taken inversely . If A B C D , then also B : A :: D : C. Let mA ...
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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