Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 páginas |
Dentro del libro
Resultados 6-10 de 34
Página 35
... shall be equal to в L , and K D to DL . Wherefore of the triangle B D L , the fides D L , LB fhall be equal to the third fide B D ; which is impoffible [ by 20. 1. ] . Therefore the lines A B , CD , drawn from angles lefs than two right ...
... shall be equal to в L , and K D to DL . Wherefore of the triangle B D L , the fides D L , LB fhall be equal to the third fide B D ; which is impoffible [ by 20. 1. ] . Therefore the lines A B , CD , drawn from angles lefs than two right ...
Página 47
... shall be equal to a given right - lined angle , and the farallelogram shall be equal to a given triangle . * Book F. the right line HF falls upon the parallels Book I. 47 Euclid's Elements .
... shall be equal to a given right - lined angle , and the farallelogram shall be equal to a given triangle . * Book F. the right line HF falls upon the parallels Book I. 47 Euclid's Elements .
Página 71
... shall divide the triangle ABC into two equal parts . Bifect [ by 10. 1. ] the fide A C of the triangle in the point E , and join the right line EB ; then if the point E falls in the point D , the thing is done ; for [ by 38. 1. ) the ...
... shall divide the triangle ABC into two equal parts . Bifect [ by 10. 1. ] the fide A C of the triangle in the point E , and join the right line EB ; then if the point E falls in the point D , the thing is done ; for [ by 38. 1. ) the ...
Página 90
... shall be equal to the fquare of the other part . PROP . XII . THEOR . In obtufe - angled triangles , the fquare of the fide oppofite to the obtufe angle , is greater than the fquares of the fides containing the obtufe angle , by twice ...
... shall be equal to the fquare of the other part . PROP . XII . THEOR . In obtufe - angled triangles , the fquare of the fide oppofite to the obtufe angle , is greater than the fquares of the fides containing the obtufe angle , by twice ...
Página 152
... shall cut the right line CD in the point D. Make [ by 14. 2. ] DC fuch , that its fquare fhall be equal to the rectangle un- der A D , DB ; then will c be the point required . For if two right lines A C , B C be drawn to it , the angle ...
... shall cut the right line CD in the point D. Make [ by 14. 2. ] DC fuch , that its fquare fhall be equal to the rectangle un- der A D , DB ; then will c be the point required . For if two right lines A C , B C be drawn to it , the angle ...
Otras ediciones - Ver todas
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Página 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 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...