Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 16
... divided into 4 , 8 , 16 , 32 , & c . equal parts , viz . by bifecting each part again . But from Euclid's poftulatums cannot be obtained the divifion generally of an angle into any other num- ber of equal parts , as 3 , 5 , 6 , 7 , 5c ...
... divided into 4 , 8 , 16 , 32 , & c . equal parts , viz . by bifecting each part again . But from Euclid's poftulatums cannot be obtained the divifion generally of an angle into any other num- ber of equal parts , as 3 , 5 , 6 , 7 , 5c ...
Page 55
... divided into three triangles ; if it has fix fides , it may be divided into four triangles , and so on . But fince [ by 32. 1. ] the angles of all these triangles are equal to twice as many right angles as there are triangles , every ...
... divided into three triangles ; if it has fix fides , it may be divided into four triangles , and so on . But fince [ by 32. 1. ] the angles of all these triangles are equal to twice as many right angles as there are triangles , every ...
Page 69
... divided at K into two cq a ! rats ; this half K will be greater than the perp ndicular draw . fom : D to AM : therefore bifect [ by 9. 1.1 th bfe BC of the given triangle in the point D ; and about the centre D , with a diftarce equal ...
... divided at K into two cq a ! rats ; this half K will be greater than the perp ndicular draw . fom : D to AM : therefore bifect [ by 9. 1.1 th bfe BC of the given triangle in the point D ; and about the centre D , with a diftarce equal ...
Page 73
... divided into two equal parts , by a right line drawn from a given point in the middle of its fide . Which was to be done . The problem is almoft as eafily refolved , when the given point is not in the middle of one of the fides ; for it ...
... divided into two equal parts , by a right line drawn from a given point in the middle of its fide . Which was to be done . The problem is almoft as eafily refolved , when the given point is not in the middle of one of the fides ; for it ...
Page 74
... divided into any parts whatsoever , the rectangle contained under the two right lines is equal to all the rectangles contained under the undivided line , and the feveral fegments or parts of the other line . L ET there be two right ...
... divided into any parts whatsoever , the rectangle contained under the two right lines is equal to all the rectangles contained under the undivided line , and the feveral fegments or parts of the other line . L ET there be two right ...
Other editions - View all
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2016 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Page 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 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...