The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
Im Buch
Ergebnisse 1-5 von 14
Seite 188
A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed . XXII . The axis of a cylinder is the fixed straight line about which the parallelogram revolves .
A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed . XXII . The axis of a cylinder is the fixed straight line about which the parallelogram revolves .
Seite 259
Every cone is the third part of a cylinder , which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude : The cone is the third part of ...
Every cone is the third part of a cylinder , which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude : The cone is the third part of ...
Seite 260
Erect prisms upon each of these triangles of the same altitude with the cylinder ; each of these prisms is greater than half the segment of the cylinder in which it is ; because if , through the points E , F , G , H , parallels be drawn ...
Erect prisms upon each of these triangles of the same altitude with the cylinder ; each of these prisms is greater than half the segment of the cylinder in which it is ; because if , through the points E , F , G , H , parallels be drawn ...
Seite 261
Therefore this prism is greater than the cylinder of which the base is the circle ABCD . But it is also less , for it is contained within the cylinder , which is impossible . Therefore the cylinder is not less than the triple of the ...
Therefore this prism is greater than the cylinder of which the base is the circle ABCD . But it is also less , for it is contained within the cylinder , which is impossible . Therefore the cylinder is not less than the triple of the ...
Seite 262
Cones and cylinders of the same altitude , are to one another as their bases . Let the cones and cylinders , of which the bases are the circles ABCD , EFGH , and the axes KL , MN , and AC , EG the diameters of their bases , be of the ...
Cones and cylinders of the same altitude , are to one another as their bases . Let the cones and cylinders , of which the bases are the circles ABCD , EFGH , and the axes KL , MN , and AC , EG the diameters of their bases , be of the ...
Was andere dazu sagen - Rezension schreiben
Es wurden keine Rezensionen gefunden.
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABCD added altitude angle ABC angle BAC arch base Book Book XI centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Beliebte Passagen
Seite 47 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.
Seite 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Seite 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Seite 54 - 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...
Seite 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Seite 153 - 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.
Seite 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Seite 28 - 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.
Seite 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.
Seite 5 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Bibliografische Informationen
| Titel | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
| Autor/in | Euclid |
| Herausgeber | Robert Simson |
| Verlag | Bell & Bradfute, 1835 |
| Original von | Harvard University |
| Digitalisiert | 6. Mai 2008 |
| Länge | 513 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |