Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Seite 172
... inscribed in the circle A B C. B D A H Hence an equilateral triangle may be eafily infcribed in a given circle ; for it C is but applying A D equal to the femidi- ameter A H of the circle ; and then again , applying BD equal to AH , and ...
... inscribed in the circle A B C. B D A H Hence an equilateral triangle may be eafily infcribed in a given circle ; for it C is but applying A D equal to the femidi- ameter A H of the circle ; and then again , applying BD equal to AH , and ...
Seite 174
... [ by 5. def . 4. ] be inscribed in the triangle AB C. F Therefore the circle EFG is infcribed in the given tri- angle A B C. Which was to be done . PROP . PROP . V. PROBL : To circumfcribe a circle about 174 Book IV . Euclid's Elements .
... [ by 5. def . 4. ] be inscribed in the triangle AB C. F Therefore the circle EFG is infcribed in the given tri- angle A B C. Which was to be done . PROP . PROP . V. PROBL : To circumfcribe a circle about 174 Book IV . Euclid's Elements .
Seite 176
... inscribe a square in a given circle . Let the given circle be A B C D : it is required to infcribe a fquare in the circle A B C D. Draw [ by 11. 1. ] two diameters A C , BD at right an- gles to one another ; and join A B2 B C , CD , DA ...
... inscribe a square in a given circle . Let the given circle be A B C D : it is required to infcribe a fquare in the circle A B C D. Draw [ by 11. 1. ] two diameters A C , BD at right an- gles to one another ; and join A B2 B C , CD , DA ...
Seite 182
... inscribed in the circle A B C D. Note also that F G is the fide of a regular decagon or figure of ten equal fides and angles infcribed in that circle . The demonftration easily follows from the ninth and tenth propofi- tions of the ...
... inscribed in the circle A B C D. Note also that F G is the fide of a regular decagon or figure of ten equal fides and angles infcribed in that circle . The demonftration easily follows from the ninth and tenth propofi- tions of the ...
Seite 184
... inscribe a circle in the penta- gon A B C D E. Bifect [ by 9 . right lines CF , DF . meet , draw the right B H M E 1. ] each of the angles B C D , CDE by the And from the point F wherein they lines F B , F A , FE . And becaufe B C is ...
... inscribe a circle in the penta- gon A B C D E. Bifect [ by 9 . right lines CF , DF . meet , draw the right B H M E 1. ] each of the angles B C D , CDE by the And from the point F wherein they lines F B , F A , FE . And becaufe B C is ...
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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...