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 66
... construction being made , it may , as before , be demonstrated , that AB is double of AF , and CD double of CG , and that the squares of EF , FA are equal to the squares of EG , GC ; of which the square of FE is equal to the square of ...
... construction being made , it may , as before , be demonstrated , that AB is double of AF , and CD double of CG , and that the squares of EF , FA are equal to the squares of EG , GC ; of which the square of FE is equal to the square of ...
Página 67
... construction being made , EH is less than EK ; Because BC is greater than FG , BH likewise is greater than KF but the squares of BH , HE are equal to the squares of FK , KE , of which the square of BH is greater than the square of FK ...
... construction being made , EH is less than EK ; Because BC is greater than FG , BH likewise is greater than KF but the squares of BH , HE are equal to the squares of FK , KE , of which the square of BH is greater than the square of FK ...
Página 80
... construction will serve for describing a circle whose circum- ference shall pass through three given points , A , B , C. PROP . II . PROB . To draw a straight line from a given point either without or in the circumfe- rence , which ...
... construction will serve for describing a circle whose circum- ference shall pass through three given points , A , B , C. PROP . II . PROB . To draw a straight line from a given point either without or in the circumfe- rence , which ...
Página 81
... construction , each of the halves AD , DB may be divided into two equal parts ; and thus , by successive subdivisions , a given arc may be divided into four , eight , sixteen , & c . equal parts . PROP . IV . PROB . Upon a given ...
... construction , each of the halves AD , DB may be divided into two equal parts ; and thus , by successive subdivisions , a given arc may be divided into four , eight , sixteen , & c . equal parts . PROP . IV . PROB . Upon a given ...
Página 116
... . ) , because the perpendiculars are both equal and parallel to one another . Then , if the same construction be made as in the proposition , the demonstration will be the same . PROP . II . THEOR . If a straight line 116 ELEMENTS.
... . ) , because the perpendiculars are both equal and parallel to one another . Then , if the same construction be made as in the proposition , the demonstration will be the same . PROP . II . THEOR . If a straight line 116 ELEMENTS.
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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