Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
Im Buch
Ergebnisse 1-5 von 29
Seite 10
Which was to be demonstrated , w Some , for want of making a difference between a geometrical congruency and a mechanical one ; that is , between an intellectual or mental one , and an actual sensual one made with the hands and the eyes ...
Which was to be demonstrated , w Some , for want of making a difference between a geometrical congruency and a mechanical one ; that is , between an intellectual or mental one , and an actual sensual one made with the hands and the eyes ...
Seite 60
... be equal to two right angles ; and the difference of the angles contained under the equal fides , will be equal to the difference of the said acute and oblique angles , Let 1 eeach ; eLet Ą B C , DET be two 60 ADDITIONS . Book I.
... be equal to two right angles ; and the difference of the angles contained under the equal fides , will be equal to the difference of the said acute and oblique angles , Let 1 eeach ; eLet Ą B C , DET be two 60 ADDITIONS . Book I.
Seite 61
... DFE will be equal to two right angles ; and the difference of the angles A B C , DEF , contained by the equal fides A B , BC , and DE , EF , will be equal to the difference of the obtuse and acute angles A CE , DFE , opposite to the ...
... DFE will be equal to two right angles ; and the difference of the angles A B C , DEF , contained by the equal fides A B , BC , and DE , EF , will be equal to the difference of the obtuse and acute angles A CE , DFE , opposite to the ...
Seite 62
Consequently , the difference of the angles D E F and A B C , will be equal to the difference of the angles A CB , EFD . Therefore if two triangles have two sides of the one equal to two sides of the other , each to each ; and one angle ...
Consequently , the difference of the angles D E F and A B C , will be equal to the difference of the angles A CB , EFD . Therefore if two triangles have two sides of the one equal to two sides of the other , each to each ; and one angle ...
Seite 63
Therefore the angle C D F exceeds the angle Fa c by twice the angle BFc ; and so the angle byc is one half their difference . Secondly , Let the perpendicular F c fall without the triangle A FD . Then because the external angle A D F of ...
Therefore the angle C D F exceeds the angle Fa c by twice the angle BFc ; and so the angle byc is one half their difference . Secondly , Let the perpendicular F c fall without the triangle A FD . Then because the external angle A D F of ...
Was andere dazu sagen - Rezension schreiben
Es wurden keine Rezensionen gefunden.
Andere Ausgaben - Alle anzeigen
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 ABCD added alſo altitude baſe becauſe centre circle circumference common cone continue cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid exceeds fall fame fides figure firſt folid fore four fourth given right line greater half inſcribed join leſs magnitudes manner meet multiple oppoſite parallel parallelogram perpendicular plane polygon priſms PROP proportional propoſition proved pyramid ratio rectangle remaining angle right angles right line A B right lined figure ſame ſay ſecond ſegment ſhall ſides ſimilar ſince ſolid ſome ſphere ſquare ſtand ſum taken THEOR theſe third thoſe thro touch triangle triangle ABC twice vertex Wherefore whole whoſe baſe
Beliebte Passagen
Seite 245 - 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 28 - 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 246 - 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 16 - 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 30 - 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 54 - 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 389 - 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 108 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Seite 128 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 181 - 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...