Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Ergebnisse 6-10 von 77
Seite 312
... plane . 4. A plane is perpendicular to a plane , when the right lines drawn in one plane perpendicular to the common fec- tion of the planes be alfo at right angles to the other plane . 5. The inclination of a right line to a plane , is ...
... plane . 4. A plane is perpendicular to a plane , when the right lines drawn in one plane perpendicular to the common fec- tion of the planes be alfo at right angles to the other plane . 5. The inclination of a right line to a plane , is ...
Seite 313
... plane . Or thus , a folid angle is that which is con- tained under more than two plane - angles not lying in the fame plane , and ftanding at one point . 12. A pyramid is a folid figure contained under several planes ftanding upon a plane ...
... plane . Or thus , a folid angle is that which is con- tained under more than two plane - angles not lying in the fame plane , and ftanding at one point . 12. A pyramid is a folid figure contained under several planes ftanding upon a plane ...
Seite 314
... plane , moves from one point of the circumference of a circle in that plane , quite round the circumference , returning again to the point from whence it first moved , the folid contained under the fuperficies generated by that moving ...
... plane , moves from one point of the circumference of a circle in that plane , quite round the circumference , returning again to the point from whence it first moved , the folid contained under the fuperficies generated by that moving ...
Seite 315
... plane , and the other elevated above it . For if poffible let the part A B of the right line A B C fie in a plane underneath , and the other part BC be ele- vated above it . Then will fome right line being the di- rect continuation of ...
... plane , and the other elevated above it . For if poffible let the part A B of the right line A B C fie in a plane underneath , and the other part BC be ele- vated above it . Then will fome right line being the di- rect continuation of ...
Seite 316
... plane , alfo every triangle lies in one plane . A E D F G For take any points F , G , in E B , E C. Join CB , FG , and draw F H , GK : First , I fay the trian- gle EBC lies in one plane : For if one part FHC or GBK of the triangle E B C ...
... plane , alfo every triangle lies in one plane . A E D F G For take any points F , G , in E B , E C. Join CB , FG , and draw F H , GK : First , I fay the trian- gle EBC lies in one plane : For if one part FHC or GBK of the triangle E B C ...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
A B C D alfo alſo angle ABC becauſe the angle bifected centre circle A B C circumference cone confequent cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid EUCLID's ELEMENTS fame altitude fame multiple fame ratio fame reafon fecond fegment femidiameter fhall fides A B fimilar fince firft firſt fixth folid angle folid parallelepipedon fome fphere ftand given circle given right line given triangle greater infcribed interfect join leffer lefs leſs parallel parallelogram perpendicular polygon prifm PROP propofition proportional pyramid rectangle contained regular polygon remaining angle right angles right line A B right lined figure right-lined SCHOLIUM ſquare thefe THEOR theſe thofe thoſe trapezium triangle ABC twice the fquare vertex the point Wherefore whofe bafe whoſe baſe
Beliebte Passagen
Seite 247 - 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 - 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...
Seite 248 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.
Seite 18 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Seite 32 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.
Seite 56 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 391 - KL: but the cylinder CM is equal to the cylinder EB, and the axis LN to the axis GH; therefore as the cylinder EB to...
Seite 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Seite 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 183 - FK : in the same manner it may be demonstrated, that FL, FM, FG are each of them equal to FH, or FK : therefore the five straight lines FG, FH, FK, FL, FM are equal to one another : wherefore the circle described from the centre F, at the distance of...