Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Seite 74
... contained under the two right lines , comprehend- ing a right angle a . 2. In every parallelogram , any one of the parallelograms that are about a diameter , with the two complements , is ... rectangle which is contained [ 74 ] EUCLID's ...
... contained under the two right lines , comprehend- ing a right angle a . 2. In every parallelogram , any one of the parallelograms that are about a diameter , with the two complements , is ... rectangle which is contained [ 74 ] EUCLID's ...
Seite 75
... rectangle con- tained under A , D E , and to that which is contained under A , E C. K L H A For [ by prop . 11. b . I ... contained under BA , A C , are equal to the fquare of the right line A B. For brevity's fake , we call the fquare ...
... rectangle con- tained under A , D E , and to that which is contained under A , E C. K L H A For [ by prop . 11. b . I ... contained under BA , A C , are equal to the fquare of the right line A B. For brevity's fake , we call the fquare ...
Seite 76
... contained under the right lines A B , AC , together with the rectangle contained under A B , BC , is equal to the fqua e of a B. D F If the efore a right line be any how divided into two parts , the rectangles contained under the whole ...
... contained under the right lines A B , AC , together with the rectangle contained under A B , BC , is equal to the fqua e of a B. D F If the efore a right line be any how divided into two parts , the rectangles contained under the whole ...
Seite 77
... rectangles AD , CE , and AE is the rectangle contained under the right lines A B , BC ; for it is contained under the right lines A B , B E , whereof B E is equal to BC : But the rect- angle A D is contained under A C , CB , fince D C ...
... rectangles AD , CE , and AE is the rectangle contained under the right lines A B , BC ; for it is contained under the right lines A B , B E , whereof B E is equal to BC : But the rect- angle A D is contained under A C , CB , fince D C ...
Seite 78
... rectangle AG [ by 43. 1. ] is equal to the rectangle G E , and A G is contain- ed under the right lines A C , CB ; for G C is equal to CB ; therefore GE is equal to the rectangle contained under AC , CB : Wherefore the rectangles AG ...
... rectangle AG [ by 43. 1. ] is equal to the rectangle G E , and A G is contain- ed under the right lines A C , CB ; for G C is equal to CB ; therefore GE is equal to the rectangle contained under AC , CB : Wherefore the rectangles AG ...
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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
A B C D alfo alſo angle ABC becauſe the angle bifected centre circle A B C circumference cone confequent cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid EUCLID's ELEMENTS fame altitude fame multiple fame ratio fame reafon fecond fegment femidiameter fhall fides A B fimilar fince firft firſt fixth folid angle folid parallelepipedon fome fphere ftand given circle given right line given triangle greater infcribed interfect join leffer lefs leſs parallel parallelogram perpendicular polygon prifm PROP propofition proportional pyramid rectangle contained regular polygon remaining angle right angles right line A B right lined figure right-lined SCHOLIUM ſquare thefe THEOR theſe thofe thoſe trapezium triangle ABC twice the fquare vertex the point Wherefore whofe bafe 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...