Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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I. 18 . for solid similar , r . Similar solid . P. 441. at the Top for Book III . r . Book VI . P. 443. at the Top , ri Book XII . P. 446,447 , 448. at the Top , r . Book VI . P. 452 , 453. at the Top , r . Book XI .
I. 18 . for solid similar , r . Similar solid . P. 441. at the Top for Book III . r . Book VI . P. 443. at the Top , ri Book XII . P. 446,447 , 448. at the Top , r . Book VI . P. 452 , 453. at the Top , r . Book XI .
Seite 110
Similar fegments of circles are those which receive equal angles , or whereof the angles in them are equal . PROPOSITION 1. PROBLEM .-To find the centre of a given circled . D Let ABC be a given circle : It is required to find the ...
Similar fegments of circles are those which receive equal angles , or whereof the angles in them are equal . PROPOSITION 1. PROBLEM .-To find the centre of a given circled . D Let ABC be a given circle : It is required to find the ...
Seite 133
Two similar and unequal segments of circles cannot be set upon the same righı line , on the same side of it . For if this be possible , let two unequal segments , ACB , A D B , of two circles ftand upon the same right line A B , both on ...
Two similar and unequal segments of circles cannot be set upon the same righı line , on the same side of it . For if this be possible , let two unequal segments , ACB , A D B , of two circles ftand upon the same right line A B , both on ...
Seite 134
Similar segments of circles , which are upon equal right lines , are equal to one another . For let A E B , CFD be similar segments of circles standing upon the equal right lines A B , CD : I say , the segments A E B , CFD are equal to ...
Similar segments of circles , which are upon equal right lines , are equal to one another . For let A E B , CFD be similar segments of circles standing upon the equal right lines A B , CD : I say , the segments A E B , CFD are equal to ...
Seite 251
If a perpendicular be drawn from the right angle to ibe base of a right angled triangle : this perpendicular will divide that right angled triangle into two other triangles ; each of which will be similar to one another , and to the ...
If a perpendicular be drawn from the right angle to ibe base of a right angled triangle : this perpendicular will divide that right angled triangle into two other triangles ; each of which will be similar to one another , and to the ...
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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 cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid exceeds fall fame fides figure firſt folid fore 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 247 - 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 30 - 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 248 - 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 18 - 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 32 - 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 56 - 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 391 - 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 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Seite 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 183 - 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...