Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite xv
Have almost prepared for the Press a Treatise of a geometrical and mechanical Constructions of Problems , with the after - written Title , which I intend to publish , if I can meet with suitable Encouragement , and can get enough Hands ...
Have almost prepared for the Press a Treatise of a geometrical and mechanical Constructions of Problems , with the after - written Title , which I intend to publish , if I can meet with suitable Encouragement , and can get enough Hands ...
Seite 4
34. All four - fided figures besides these may be called trapeziunis . 35. Parallels are right lines , which being in the same plane , and produced infinitely either way , will not meet one another either way " ...
34. All four - fided figures besides these may be called trapeziunis . 35. Parallels are right lines , which being in the same plane , and produced infinitely either way , will not meet one another either way " ...
Seite 5
... may be infinitely produced both ways , and never meet , and yet not be such as Èuclid calls parallels . s This eighth axiom is universally convertible , although Proclus , Borellus , Taquet , & c . say it is not .
... may be infinitely produced both ways , and never meet , and yet not be such as Èuclid calls parallels . s This eighth axiom is universally convertible , although Proclus , Borellus , Taquet , & c . say it is not .
Seite 6
gles , those right lines , being infinitely produced , do meet on that fide where the angles are less than two right angles " , 12. Two right lines do not comprehend a space . - ge' A t All these axioms are so evident , when the words ...
gles , those right lines , being infinitely produced , do meet on that fide where the angles are less than two right angles " , 12. Two right lines do not comprehend a space . - ge' A t All these axioms are so evident , when the words ...
Seite 32
For if it be not parallel , the lines A B , dc produced will meet either towards B D or A C ; let them be produced towards A E B D , and meet in the point G. Now the angle A Ef being the external angle of the triangle с D EGF ...
For if it be not parallel , the lines A B , dc produced will meet either towards B D or A C ; let them be produced towards A E B D , and meet in the point G. Now the angle A Ef being the external angle of the triangle с D EGF ...
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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...