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 23
... proposition , all the angles of these triangles are equal to twice as many right angles as there are tri- angles , that is , as there are sides of the figure ; and the same angles are equal to the angles of the figure , together with ...
... proposition , all the angles of these triangles are equal to twice as many right angles as there are tri- angles , that is , as there are sides of the figure ; and the same angles are equal to the angles of the figure , together with ...
Página 24
... proposition is applied to polygons , which have re - entrant an- gles , as ABC , each re - entrant an- gle must be regarded as greater than two right angles . And , by joining BD , BE , BF , the figure is divided into four triangles ...
... proposition is applied to polygons , which have re - entrant an- gles , as ABC , each re - entrant an- gle must be regarded as greater than two right angles . And , by joining BD , BE , BF , the figure is divided into four triangles ...
Página 45
... proposition , for instance , let the seg- ments of BC be denoted by b , c , and d ' ; then , A ( b + c + d ) = Ab + Ac + Ad . PROP . II . THEOR . If a straight line be divided into any two parts , the rectangles contained by the whole ...
... proposition , for instance , let the seg- ments of BC be denoted by b , c , and d ' ; then , A ( b + c + d ) = Ab + Ac + Ad . PROP . II . THEOR . If a straight line be divided into any two parts , the rectangles contained by the whole ...
Página 46
... proposition let AB be denoted by a , and the segments AC and CB , by b and c ; then a = b + c : therefore , multiplying both members of this equality by c , we shall have ac = bc + c2 . PROP . IV . THEOR . If a straight line be divided ...
... proposition let AB be denoted by a , and the segments AC and CB , by b and c ; then a = b + c : therefore , multiplying both members of this equality by c , we shall have ac = bc + c2 . PROP . IV . THEOR . If a straight line be divided ...
Página 47
... proposition it is manifest , that the difference of the squares of two unequal lines , AC , CD , is equal to the rectangle contain- " ed by their sum and difference , or that AC2 - CD2 = ( AC + CD ) ( AC- " CD ) . " SCHOLIUM . In this ...
... proposition it is manifest , that the difference of the squares of two unequal lines , AC , CD , is equal to the rectangle contain- " ed by their sum and difference , or that AC2 - CD2 = ( AC + CD ) ( AC- " CD ) . " SCHOLIUM . In this ...
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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