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 |
Dentro del libro
Resultados 6-10 de 50
Página 63
... radius will be also less than the sum of the smaller and the distance between the centres . For , CD is less ( 13. 1. ) than CA + AD , and for the same reason , ADZAC + CD . 2. And , conversely , if the distance between the centres of ...
... radius will be also less than the sum of the smaller and the distance between the centres . For , CD is less ( 13. 1. ) than CA + AD , and for the same reason , ADZAC + CD . 2. And , conversely , if the distance between the centres of ...
Página 64
... radius of the greater circle . 2. If the two circles will touch each other internally , then , d = R — r . And , conversely , if d = R ― r , the two circles will touch each other inter- nally . 3. If two circles touch each other ...
... radius of the greater circle . 2. If the two circles will touch each other internally , then , d = R — r . And , conversely , if d = R ― r , the two circles will touch each other inter- nally . 3. If two circles touch each other ...
Página 78
... radius drawn to the point of contact is perpendicular to the tangent , it follows that the angle included by two tangents , B B E D F E A A F B drawn from the same point , is bisected by a line drawn from the centre of the circle to ...
... radius drawn to the point of contact is perpendicular to the tangent , it follows that the angle included by two tangents , B B E D F E A A F B drawn from the same point , is bisected by a line drawn from the centre of the circle to ...
Página 90
... radius , as the square root of 2 , is to unity . PROP . VI . PROB . To describe a square about a given circle . Let ABCD be the given circle ; it is required to describe a square about it . Draw two diameters AC , BD of the circle ABCD ...
... radius , as the square root of 2 , is to unity . PROP . VI . PROB . To describe a square about a given circle . Let ABCD be the given circle ; it is required to describe a square about it . Draw two diameters AC , BD of the circle ABCD ...
Página 94
... pentagon has been inscribed . Otherwise . " Divide the radius of the given circle , so that the rectangle contained by " the whole and one of the parts may be equal to the square of the other " ( 9. 4. ) . Apply in the circle 94 ELEMENTS.
... pentagon has been inscribed . Otherwise . " Divide the radius of the given circle , so that the rectangle contained by " the whole and one of the parts may be equal to the square of the other " ( 9. 4. ) . Apply in the circle 94 ELEMENTS.
Otras ediciones - Ver todas
Términos y frases comunes
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