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 Sperical TrigonometryW.E. Dean, 1844 - 317 sider |
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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 ...
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Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |
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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 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 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
Populære avsnitt
Side 95 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 68 - THE angles in the same segment of a circle are equal to one another...
Side 23 - 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 74 - 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 78 - 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 9 - 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 75 - If a straight line touch a circle, and from the point of contact a...
Side 18 - AT a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Side 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 136 - AB is (7. 5.) to AD, as AE to AG ; and DC to CB, as GF to FE; and also CD to DA, as FG to GA ; therefore the sides of the parallelograms ABCD, AEFG about the equal angles are proportionals; and they are therefore similar to one another (1.