Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Seite 53
... same side of it be given , and two right lines be drawn from thofe points to any point in the given right line ; these two right lines taken together will be the leaft of all , when they make equal angles with the given right line . C D ...
... same side of it be given , and two right lines be drawn from thofe points to any point in the given right line ; these two right lines taken together will be the leaft of all , when they make equal angles with the given right line . C D ...
Seite 115
... same centre . PROP . VII . THEOR . If any point except the centre be taken in the diame- ter 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 ...
... same centre . PROP . VII . THEOR . If any point except the centre be taken in the diame- ter 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 ...
Seite 132
... same segment B A ED of that circle : I say , thefe angles are equal to one another . A B F E For [ by 1. 3. ] find F the centre of the circle A B C D , and join B F , F D. Then because the angle B F D is at the centre , and the angle ...
... same segment B A ED of that circle : I say , thefe angles are equal to one another . A B F E For [ by 1. 3. ] find F the centre of the circle A B C D , and join B F , F D. Then because the angle B F D is at the centre , and the angle ...
Seite 193
... same segment of a cir- cle [ by 21. 3. ] are equal to one another , the angle A B C will be equal to the angle EFG , fince [ by conftruction ] the fegment A B C of the circle contains an angle equal to the angle E F G. And because [ by ...
... same segment of a cir- cle [ by 21. 3. ] are equal to one another , the angle A B C will be equal to the angle EFG , fince [ by conftruction ] the fegment A B C of the circle contains an angle equal to the angle E F G. And because [ by ...
Seite 215
... , when compared to one another . For let the first magnitude △ have the same ratio to the fecond B , as the third c has to the fourth D. Take E , ▻ P 4 any any equimult ples of A , C , and G Book V. 215 Euclid's Elements .
... , when compared to one another . For let the first magnitude △ have the same ratio to the fecond B , as the third c has to the fourth D. Take E , ▻ P 4 any any equimult ples of A , C , and G Book V. 215 Euclid's Elements .
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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...