Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 109
A right line is said to touch a circle , when meeting it and being produced does not cut it . 3. Circles are said to touch one another , which meeting one another do not cut one another . 4. Right lines in a circle are said to be ...
A right line is said to touch a circle , when meeting it and being produced does not cut it . 3. Circles are said to touch one another , which meeting one another do not cut one another . 4. Right lines in a circle are said to be ...
Seite 112
This theorem may be demonstrated affirmatively , thus : Let the right line A B touch two points A , B in the circumference of the circle a B , whose centre is c : I say , the right line A B falls within the circle , so that all its ...
This theorem may be demonstrated affirmatively , thus : Let the right line A B touch two points A , B in the circumference of the circle a B , whose centre is c : I say , the right line A B falls within the circle , so that all its ...
Seite 115
If two circles touch one another inwardly , they will not both have the same centre ' . any how . For let two circles A B C , cde touch one another inwardly in the point c : I say , they have not both the same : centre .
If two circles touch one another inwardly , they will not both have the same centre ' . any how . For let two circles A B C , cde touch one another inwardly in the point c : I say , they have not both the same : centre .
Seite 122
If two circles touch one another inwardly , and their centres be taken , the right line joining their centres being produced , will fall in the point wherein those circles touch one another . For let two circles ABC , AD E , touch one ...
If two circles touch one another inwardly , and their centres be taken , the right line joining their centres being produced , will fall in the point wherein those circles touch one another . For let two circles ABC , AD E , touch one ...
Seite 123
THEO R. If two circles touch one another outwardly , the right line joining their centres will pass thro ' the point wherein the circles touch one another , For let two circles . ABC , AD E , touch one another outwardly in the point A.
THEO R. If two circles touch one another outwardly , the right line joining their centres will pass thro ' the point wherein the circles touch one another , For let two circles . ABC , AD E , touch one another outwardly in the point A.
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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...