Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Seite 101
... sum of the fquares of AF , FD , AE , ED will be equal to four times the square of AB , together with twice the fquares of FB , BE . Or fince [ by 4. 2. ] four times the fquare of AB is equal to the fquare of the dia- gonal AD , the sum ...
... sum of the fquares of AF , FD , AE , ED will be equal to four times the square of AB , together with twice the fquares of FB , BE . Or fince [ by 4. 2. ] four times the fquare of AB is equal to the fquare of the dia- gonal AD , the sum ...
Seite 104
... sum of the two triangles BCD , BAD ; that is , one half the trapezium A B C D. Therefore , & c . Which was to be demonftrated . PROP . VIII . THEOR . If the middle points of the oppofite fides of any qua- drilateral figure be joined by ...
... sum of the two triangles BCD , BAD ; that is , one half the trapezium A B C D. Therefore , & c . Which was to be demonftrated . PROP . VIII . THEOR . If the middle points of the oppofite fides of any qua- drilateral figure be joined by ...
Seite 106
... FG , G H , HI , IK , K F : I fay , thrice the sum of the fquares of the fides AB , BC , CD , DE , E A of the figure will be equal to the fum of the fquares figure 106 Book II . ADDITIONS . the fquares of AE, EI, CG, I ...
... FG , G H , HI , IK , K F : I fay , thrice the sum of the fquares of the fides AB , BC , CD , DE , E A of the figure will be equal to the fum of the fquares figure 106 Book II . ADDITIONS . the fquares of AE, EI, CG, I ...
Seite 107
... sum of the fquares of the five diagonals AD , BE , AC , BD , CE . Also adding all the latter fquares together , their fum will be equal to twice the fquare of each of the five diagonals A C , B D , CE , A D , BE , together with four ...
... sum of the fquares of the five diagonals AD , BE , AC , BD , CE . Also adding all the latter fquares together , their fum will be equal to twice the fquare of each of the five diagonals A C , B D , CE , A D , BE , together with four ...
Seite 158
... sum of the three angles A B C , CD E , A FE . Again , Let the figure ABCDEFGH [ fig . 2. ] in the circle have eight fides : I fay , its four angles A , C , E , G will be equal to its four angles B , D , F , H. For For divide the figure ...
... sum of the three angles A B C , CD E , A FE . Again , Let the figure ABCDEFGH [ fig . 2. ] in the circle have eight fides : I fay , its four angles A , C , E , G will be equal to its four angles B , D , F , H. For For divide the figure ...
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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...