Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Seite 198
... polygon upon the given right line A в . First , Let the number of fides of the polygon be odd . Continue out the given right line A B to D , fo that A D be equal to a B. About the centre A with the distance A D , defcribe part of a ...
... polygon upon the given right line A в . First , Let the number of fides of the polygon be odd . Continue out the given right line A B to D , fo that A D be equal to a B. About the centre A with the distance A D , defcribe part of a ...
Seite 199
... polygon has eight fides , the arch CE must be four of eight equal parts ; that is , one half the quadrant D c . If the polygon has ten fides , the arch c E must be fix of ten equal parts , or three of five that the quadrant D C is ...
... polygon has eight fides , the arch CE must be four of eight equal parts ; that is , one half the quadrant D c . If the polygon has ten fides , the arch c E must be fix of ten equal parts , or three of five that the quadrant D C is ...
Seite 200
... polygon , and A B н another angle of the polygon . And fince the femidiameter of a circle drawn to any one angle of a regular polygon infcri- bed in a circle bifects that angle , therefore the point F will be the centre of a circle , in ...
... polygon , and A B н another angle of the polygon . And fince the femidiameter of a circle drawn to any one angle of a regular polygon infcri- bed in a circle bifects that angle , therefore the point F will be the centre of a circle , in ...
Seite 201
... polygon ADEFBGHICA will have nine equal fides . For because the four angles BAG , GAH , HAI , IAC [ by E fuppofition ] are each equal to the angle ABC at the circumference , F and alfo the four angles F C B , D ECF , EC D , DCA at the ...
... polygon ADEFBGHICA will have nine equal fides . For because the four angles BAG , GAH , HAI , IAC [ by E fuppofition ] are each equal to the angle ABC at the circumference , F and alfo the four angles F C B , D ECF , EC D , DCA at the ...
Seite 202
... polygon of fixteen equal fides will be less than eight of the fegments A B , whereby the circle differs from the regular polygon A B C D E F G H of eight fides . Confequently a regular polygon of fixteen fides is nearer to the circle in ...
... polygon of fixteen equal fides will be less than eight of the fegments A B , whereby the circle differs from the regular polygon A B C D E F G H of eight fides . Confequently a regular polygon of fixteen fides is nearer to the circle in ...
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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 - 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...