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 GeometryJ.B. Lippincott & Company, 1860 - 317 sider |
Inni boken
Resultat 1-5 av 7
Side 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 ...
Side 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 ...
Side 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 ...
Side 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 ...
... 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 ...
Side 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 ...
Andre utgaver - Vis alle
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |
Elements of Geometry: Containing the First Six Books of Euclid : with a ... John Playfair Uten tilgangsbegrensning - 1837 |
Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |
Vanlige uttrykk og setninger
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle BCD 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 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 spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 49 - 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.
Side 9 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 27 - 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.
Side 17 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Side 13 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Side 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.
Side 55 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Side 24 - ... sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Side 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 78 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.