Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite xv
... or folid , except a few of Euclid's Propositions , and half a Dozen of the principal Properties of the Three Conick Sections , and executed by a few fimple and common Instruments , without Reference to any other Treatise .
... or folid , except a few of Euclid's Propositions , and half a Dozen of the principal Properties of the Three Conick Sections , and executed by a few fimple and common Instruments , without Reference to any other Treatise .
Seite 35
Again , B let fo be cut in half in H , and equal to hf let be put f b , and to HG , D GD ; then draw BD : I say , that C L the lines A B , CD may for ever be thus prolonged , yet never fhall they meet together .
Again , B let fo be cut in half in H , and equal to hf let be put f b , and to HG , D GD ; then draw BD : I say , that C L the lines A B , CD may for ever be thus prolonged , yet never fhall they meet together .
Seite 42
35. ] is equal to the parallelagram D BCF , for they stand both upon the same base á c , and are between the same pas C rallelş B C , EF . But the triangle E angle A B C is the one half of the 42 Euclid's Elements . Book I.
35. ] is equal to the parallelagram D BCF , for they stand both upon the same base á c , and are between the same pas C rallelş B C , EF . But the triangle E angle A B C is the one half of the 42 Euclid's Elements . Book I.
Seite 43
angle A B C is the one half of the parallelogram e BCA ; since the diameter AB cuts into halves , and the triangle DBC the one half of the parallelogram DBCF ; because [ by prop . 34. ] the diameter Dc cuts it into halves .
angle A B C is the one half of the parallelogram e BCA ; since the diameter AB cuts into halves , and the triangle DBC the one half of the parallelogram DBCF ; because [ by prop . 34. ] the diameter Dc cuts it into halves .
Seite 62
In every triangle , the angle contained under the perpendicular drawn from the angle opposite to the base upon it , and the right line bisetting that angle , will be one half the difference of the angles at the base .
In every triangle , the angle contained under the perpendicular drawn from the angle opposite to the base upon it , and the right line bisetting that angle , will be one half the difference of the angles at the base .
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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...