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 43
... given rectangle AEFH ( Th . 36. 1. ) . A E D H F K B G A polygon may be converted into an equivalent rectangle , having one of its sides of a given length . ELEMENTS OF GEOMETRY . BOOK II . DEFINITIONS . 1. OF GEOMETRY . BOOK I. 43.
... given rectangle AEFH ( Th . 36. 1. ) . A E D H F K B G A polygon may be converted into an equivalent rectangle , having one of its sides of a given length . ELEMENTS OF GEOMETRY . BOOK II . DEFINITIONS . 1. OF GEOMETRY . BOOK I. 43.
Página 44
... DEFINITIONS . 1. EVERY right angled parallelogram , or rectangle , is said to be contained by any two of the straight lines which are about one of the right an- gles . " Thus the right angled parallelogram AC is called the rectangle ...
... DEFINITIONS . 1. EVERY right angled parallelogram , or rectangle , is said to be contained by any two of the straight lines which are about one of the right an- gles . " Thus the right angled parallelogram AC is called the rectangle ...
Página 54
... are therefore equal : whence it follows that the angles BEC , DEC , are equal ; and , therefore , that the two diagonals of a rhom- bus cut each other at right angles . ELEMENTS OF GEOMETRY . BOOK III . DEFINITIONS . 1. 54 ELEMENTS , & c .
... are therefore equal : whence it follows that the angles BEC , DEC , are equal ; and , therefore , that the two diagonals of a rhom- bus cut each other at right angles . ELEMENTS OF GEOMETRY . BOOK III . DEFINITIONS . 1. 54 ELEMENTS , & c .
Página 55
... DEFINITIONS . 1. The radius of a circle is the straight line drawn from the centre to the circumference . 2. A straight line is said to touch a circle , when it meets the cir- cle , and being produced does not cut it . And that line ...
... DEFINITIONS . 1. The radius of a circle is the straight line drawn from the centre to the circumference . 2. A straight line is said to touch a circle , when it meets the cir- cle , and being produced does not cut it . And that line ...
Página 56
... definition of a circle . A E F B D Conversely . The line dividing the circle into two equal parts is a diameter . For , let AB divide the circle into two equal parts ; then , if the centre is not in AB , let AF be drawn through it ...
... definition of a circle . A E F B D Conversely . The line dividing the circle into two equal parts is a diameter . For , let AB divide the circle into two equal parts ; then , if the centre is not in AB , let AF be drawn through it ...
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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