Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Seite 150
... semidiameter of the circle be equal . Let there be a given circle A E B , whose semidiameter is the right line F E , and let C , D be two assumed points without the circle , and let two right lines CE , ED be drawn ( not cutting thro ...
... semidiameter of the circle be equal . Let there be a given circle A E B , whose semidiameter is the right line F E , and let C , D be two assumed points without the circle , and let two right lines CE , ED be drawn ( not cutting thro ...
Seite 160
... semidiameters FA , FE , F D to the points of contact . Then because [ by 5. 1. ] the an- Cgles FAE , FEA are equal to one another , as also FDE , FED . There- fore [ by 32. 1. ) twice the angle D FAE , together with the angle AFE , will ...
... semidiameters FA , FE , F D to the points of contact . Then because [ by 5. 1. ] the an- Cgles FAE , FEA are equal to one another , as also FDE , FED . There- fore [ by 32. 1. ) twice the angle D FAE , together with the angle AFE , will ...
Seite 172
... semidiameter HA , and at the centre i with the femidiameter H A make [ by 23. 1. ] the angle AHB double to one of the angles E DF of the given triangle . Apply the right line A B. E C H D F B A At the point a with the right line A B ...
... semidiameter HA , and at the centre i with the femidiameter H A make [ by 23. 1. ] the angle AHB double to one of the angles E DF of the given triangle . Apply the right line A B. E C H D F B A At the point a with the right line A B ...
Seite 182
... semidiameter a F in E. Join E , B. And upon a c from E lay off E G equal to E B. And draw the right line BG : which will be the fide of the pentagon required . Then from в apply в і , в н equal to BG , as also IK , KL , LH : And the ...
... semidiameter a F in E. Join E , B. And upon a c from E lay off E G equal to E B. And draw the right line BG : which will be the fide of the pentagon required . Then from в apply в і , в н equal to BG , as also IK , KL , LH : And the ...
Seite 187
... semidiameter of the circle . And if tangents to the circle be drawn thro ' the points A , B , C , D , E , F , an equilateral and equiangular hexagon will be circumfcribed about the circle , as is evident from what has been faid of the ...
... semidiameter of the circle . And if tangents to the circle be drawn thro ' the points A , B , C , D , E , F , an equilateral and equiangular hexagon will be circumfcribed about the circle , as is evident from what has been faid of the ...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
alſo angle ABC becauſe the angle biſected centre circle ABCD circumference cone conſequent conſtruction cylinder demonftrated deſcribed diameter equal angles equal fides equiangular equimultiples Euclid fame altitude fame ratio fame reaſon fides A B fimilar fince firſt fixth fore four right given circle given right line given triangle greater inſcribed interfect join leſs oppoſite parallel parallelepipedon parallelogram perpendicular plane point F polygon priſms PROP proportional propoſition rectangle rectangle contained remaining angle right angles right line A B right lined figure right-lined ſame ſame multiple ſay SCHOLIUM ſecond ſector ſegment ſemidiameter ſhall ſide ſince ſolid ſome ſphere ſquares of A C ſtand ſuch ſum THEOR theſe thoſe thro trapezium triangle ABC twice the ſquare vertex the point Wherefore 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...