Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 Seiten |
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Seite 9
... angle of the ether , viz . that which is contained under the equal lines ; then shall the base of the one be equal to the base of the other ; and one triangle equal to the other triangle ; and the remaining ... remaining angles of the other ...
... angle of the ether , viz . that which is contained under the equal lines ; then shall the base of the one be equal to the base of the other ; and one triangle equal to the other triangle ; and the remaining ... remaining angles of the other ...
Seite 10
... angle ABC to the angle D E F , and the angle ACB to the angle DFE . B For if the triangle ABC be applied to the ... remaining angles will agree with the remaining an- gles , and therefore fhall be equal to them , viz . the angle ABC to ...
... angle ABC to the angle D E F , and the angle ACB to the angle DFE . B For if the triangle ABC be applied to the ... remaining angles will agree with the remaining an- gles , and therefore fhall be equal to them , viz . the angle ABC to ...
Seite 11
... angle AG B. But fince the whole line AF is equal to the whole line A G , and A B is equal to A C ; therefore the remainder BF will be equal to the remainder CG [ by ax . 3 ... angle B C F ; the remaining angle Book I. IL Euclid's Elements .
... angle AG B. But fince the whole line AF is equal to the whole line A G , and A B is equal to A C ; therefore the remainder BF will be equal to the remainder CG [ by ax . 3 ... angle B C F ; the remaining angle Book I. IL Euclid's Elements .
Seite 12
... remaining angle A B C [ by ax . 3. ] will be equal to the remaining angle ACB ; and they are at the bafe of the triangle A B C. But alfo it has been de- monftrated , that the angle F B C is equal to the angle G C B , and they are under ...
... remaining angle A B C [ by ax . 3. ] will be equal to the remaining angle ACB ; and they are at the bafe of the triangle A B C. But alfo it has been de- monftrated , that the angle F B C is equal to the angle G C B , and they are under ...
Seite 16
... remain [ by axiom 3. ] the angles E A F , E D F equal . Which was to be demonftrated . .. PROP . IX . PRO BL . To bifect or cut a given right - lined angle into two equal parts . Let the given right - lined angle be BAC ; it is required ...
... remain [ by axiom 3. ] the angles E A F , E D F equal . Which was to be demonftrated . .. PROP . IX . PRO BL . To bifect or cut a given right - lined angle into two equal parts . Let the given right - lined angle be BAC ; it is required ...
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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...