Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 109
A segment of a circle is a figure contained under a right line and a part of the circumference of a circle b . 7. An angle of a fegment is that which is contained under a right line and the circumference of a circle . 8.
A segment of a circle is a figure contained under a right line and a part of the circumference of a circle b . 7. An angle of a fegment is that which is contained under a right line and the circumference of a circle . 8.
Seite 110
But when the right lines containing such an angle do cut off part of the circumference of the circle , the angle is faid to Itand upon that part cut off . 10. A sector of a circle is the figure comprehended between two right lines drawn ...
But when the right lines containing such an angle do cut off part of the circumference of the circle , the angle is faid to Itand upon that part cut off . 10. A sector of a circle is the figure comprehended between two right lines drawn ...
Seite 111
The praxis of this problem may be somewhat Shorter , thus : Open the compasses to any D convenient distance that will cut the given circle , and setting one foot in the circumference at the point A describe an arch b c with the other ...
The praxis of this problem may be somewhat Shorter , thus : Open the compasses to any D convenient distance that will cut the given circle , and setting one foot in the circumference at the point A describe an arch b c with the other ...
Seite 112
Therefore the right line drawn from the point A to B does not fall without the circle , nor does it fall in the circumference . Consequently it must necessarily fall within the circle , If therefore any two points be taken in the ...
Therefore the right line drawn from the point A to B does not fall without the circle , nor does it fall in the circumference . Consequently it must necessarily fall within the circle , If therefore any two points be taken in the ...
Seite 115
If any point except the centre be taken in the diameter of a circle , and any right lines drawn from it do fall upon the circumference of the circle , the greatest of them will be that wherein is the centre , and the least ...
If any point except the centre be taken in the diameter of a circle , and any right lines drawn from it do fall upon the circumference of the circle , the greatest of them will be that wherein is the centre , and the least ...
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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...