Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite xii
Moreover , I do not know how juftly the Author of the Fifth Book can apply his Propositions of it to Thew the Proportionality of Lines , and plain Figures in the a a Sixth Book ; and of Lines , Surfaces , and Sixth xii To the READER :
Moreover , I do not know how juftly the Author of the Fifth Book can apply his Propositions of it to Thew the Proportionality of Lines , and plain Figures in the a a Sixth Book ; and of Lines , Surfaces , and Sixth xii To the READER :
Seite xiii
... or Solids , & c . the whole Doctrine of the Proportionality of Magnitudes contained in the Fifth Book , may be clearly , briefly , and easily , stated and demonstrated , whether the Magnitudes be commensurable or incommensurable ...
... or Solids , & c . the whole Doctrine of the Proportionality of Magnitudes contained in the Fifth Book , may be clearly , briefly , and easily , stated and demonstrated , whether the Magnitudes be commensurable or incommensurable ...
Seite 147
proportionality of the fides of cquiangular triangles , and by prop . xvi . of that book , But Euclid wanted these propositions before , for demonftrating the tenth and eleventh of the fourth book ; and therefore he was obliged to ...
proportionality of the fides of cquiangular triangles , and by prop . xvi . of that book , But Euclid wanted these propositions before , for demonftrating the tenth and eleventh of the fourth book ; and therefore he was obliged to ...
Seite 167
... because their demonstrations are porter and much easier from the proportionality of the sides of equiangular triangles , and the equality of the rectangles under the means and extremes , than by the propositions of the second book .
... because their demonstrations are porter and much easier from the proportionality of the sides of equiangular triangles , and the equality of the rectangles under the means and extremes , than by the propositions of the second book .
Seite 208
Then it necessarily follows that those four proposed magnitudes will be proportional ; fo that from hence it most clearly appears how ... natural , and easy Sign of proportionality , derived from the before mentioned two propofitions .
Then it necessarily follows that those four proposed magnitudes will be proportional ; fo that from hence it most clearly appears how ... natural , and easy Sign of proportionality , derived from the before mentioned two propofitions .
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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...