Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Seite 10
... angle ABC to the angle DEF , and the angle ACB to the angle DFE . B For if the triangle A B C be applied to the ... because A B is equal to DE : But since CE F the right line A B agrees with DE , the right line a c shall also agree ...
... angle ABC to the angle DEF , and the angle ACB to the angle DFE . B For if the triangle A B C be applied to the ... because A B is equal to DE : But since CE F the right line A B agrees with DE , the right line a c shall also agree ...
Seite 12
... angle A B C [ by ax . 3. ] will be equal to the remaining angle ACB ; and they are at the base of the triangle A B C ... because , says he , it is certain , that Euclid never laid down an elementary propofition useless in any part ...
... angle A B C [ by ax . 3. ] will be equal to the remaining angle ACB ; and they are at the base of the triangle A B C ... because , says he , it is certain , that Euclid never laid down an elementary propofition useless in any part ...
Seite 13
... because A C is equal to AD , the angle ACD is equal to the angle ADC [ by prop . 5. ] wherefore the angle ADC is greater than the angle DCB , and the angle CDB is much greater than the angle D C B. Again , because the right line CB is ...
... because A C is equal to AD , the angle ACD is equal to the angle ADC [ by prop . 5. ] wherefore the angle ADC is greater than the angle DCB , and the angle CDB is much greater than the angle D C B. Again , because the right line CB is ...
Seite 19
... angles ( by def . 10. ] but if not , let the right line E B be drawn from the point s at right E A angles to the right line DC [ by prop . 11. ] then the angles CBE , E B D are two right angles . And because the angle CBE is equal to both ...
... angles ( by def . 10. ] but if not , let the right line E B be drawn from the point s at right E A angles to the right line DC [ by prop . 11. ] then the angles CBE , E B D are two right angles . And because the angle CBE is equal to both ...
Seite 20
... as there the angle A BE is the excess , so is the fame angle A B E here the deficiency . Wherefore it necessarily follows , that both the angles A B D , A B C are equal to two right angles , the one being just as much above a right angle , ...
... as there the angle A BE is the excess , so is the fame angle A B E here the deficiency . Wherefore it necessarily follows , that both the angles A B D , A B C are equal to two right angles , the one being just as much above a right angle , ...
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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...