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 15
... the greater angle therefore the side DB is greater than the side BC ; but DB is equal to BA and AC together ; therefore BA and AC together are greater than BC . In the same manner it may be demonstrated OF GEOMETRY . BOOK I. 15.
... the greater angle therefore the side DB is greater than the side BC ; but DB is equal to BA and AC together ; therefore BA and AC together are greater than BC . In the same manner it may be demonstrated OF GEOMETRY . BOOK I. 15.
Página 16
... demonstrated , that the sides AB , are greater than CA , and BC , CA greater than AB . SCHOLIUM . BC This may be demonstrated without producing any of the sides : thus , the line BC , for example , is the shortest distance from B to C ...
... demonstrated , that the sides AB , are greater than CA , and BC , CA greater than AB . SCHOLIUM . BC This may be demonstrated without producing any of the sides : thus , the line BC , for example , is the shortest distance from B to C ...
Página 19
... demonstrated that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 15 Def . ) to one another . AB therefore is parallel to CD . PROP . XX . THEOR . If a ...
... demonstrated that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 15 Def . ) to one another . AB therefore is parallel to CD . PROP . XX . THEOR . If a ...
Página 29
... demonstrated that no other line but AD is parallel to BC ; AD is therefore parallel to it . PROP . XXXIV . THEOR . B D E Equivalent triangles on the same side of bases which are equal and in the same straight line , are between the same ...
... demonstrated that no other line but AD is parallel to BC ; AD is therefore parallel to it . PROP . XXXIV . THEOR . B D E Equivalent triangles on the same side of bases which are equal and in the same straight line , are between the same ...
Página 42
... demonstrated that it is equilateral ; it is therefore a square , and it is described upon the given straight line AB . PROP . XIX . PROB . To find the side of a square that shall be equivalent to the sum of two squares . Draw the two ...
... demonstrated that it is equilateral ; it is therefore a square , and it is described upon the given straight line AB . PROP . XIX . PROB . To find the side of a square that shall be equivalent to the sum of two squares . Draw the two ...
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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