Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 σελίδες |
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Αποτελέσματα 1 - 5 από τα 6.
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Σελίδα 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Σελίδα 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...