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 TrigonometryW.E. Dean, 1853 - 317 pagine |
Dall'interno del libro
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Pagina 196
... cylinder is the fixed straight line about which the paral- lelogram revolves . 16. The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram . 17. Similar cones and cylinders are those ...
... cylinder is the fixed straight line about which the paral- lelogram revolves . 16. The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram . 17. Similar cones and cylinders are those ...
Pagina 211
... cylinder , a straight line be drawn perpendicular to the plane of the base , it will be wholly in the cylindric superficies . Let ABCD be a cylinder of which the base is the circle AEB , DFC the circle opposite to the base , and GH the ...
... cylinder , a straight line be drawn perpendicular to the plane of the base , it will be wholly in the cylindric superficies . Let ABCD be a cylinder of which the base is the circle AEB , DFC the circle opposite to the base , and GH the ...
Pagina 212
... cylinder , for it describes that superficies ; therefore , EF is also in the superficies of the cylinder . PROP . XVII . THEOR . A cylinder and a parallelopiped having equal bases and altitudes , are equal to one another . Let ABCD be a ...
... cylinder , for it describes that superficies ; therefore , EF is also in the superficies of the cylinder . PROP . XVII . THEOR . A cylinder and a parallelopiped having equal bases and altitudes , are equal to one another . Let ABCD be a ...
Pagina 213
... cylinder , which will therefore be less than the cylinder , be- cause it is within it ( 16. 3. Sup . ) ; and if through the point R a plane RS parallel to NF be made to pass , it will cut off the parallelopiped ES equal ( 2. Cor . 8. 3 ...
... cylinder , which will therefore be less than the cylinder , be- cause it is within it ( 16. 3. Sup . ) ; and if through the point R a plane RS parallel to NF be made to pass , it will cut off the parallelopiped ES equal ( 2. Cor . 8. 3 ...
Pagina 214
... cylinder LMNO . Now , the cone ABECFD is , by hypothesis , the third part of the cylinder LMNO , therefore the pyra- mid ABECFD is greater than the cone ABCD , and it is also less , because it is inscribed in the cone , which is ...
... cylinder LMNO . Now , the cone ABECFD is , by hypothesis , the third part of the cylinder LMNO , therefore the pyra- mid ABECFD is greater than the cone ABCD , and it is also less , because it is inscribed in the cone , which is ...
Altre edizioni - Visualizza tutto
Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Visualizzazione completa - 1851 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Visualizzazione completa - 1857 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Visualizzazione completa - 1836 |
Parole e frasi comuni
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal 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 PROB PROP proportional 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 touches the circle triangle ABC triangle DEF wherefore
Brani popolari
Pagina 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Pagina 74 - THE angles in the same segment of a circle are equal to one another...
Pagina 37 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Pagina 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Pagina 29 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through EAF the point A, parallel to the straight line '
Pagina 147 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Pagina 19 - The angles which one straight line makes with another upon one side of i't, are either two right angles, or are together eqval to two right angles.
Pagina 134 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Pagina 294 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Pagina 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.