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 TrigonometryJ.P. Lippincott & Company, 1855 - 318 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. 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 ...
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 - 1855 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1847 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1839 |
Vanlige uttrykk og setninger
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition 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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 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.
Side 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.
Side 12 - 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.
Side 11 - Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Side 72 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Side 84 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 80 - 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.
Side 22 - Any two sides of a triangle are together greater than the third side.
Side 53 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.