Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 páginas |
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Resultados 6-10 de 53
Página 33
... meet . After the same manner we de- monftrate , that these lines will not meet towards a c : but right lines , which being either way produced , and do not meet , are [ by def . 35. ] parallel to one another . Therefore A B is parallel ...
... meet . After the same manner we de- monftrate , that these lines will not meet towards a c : but right lines , which being either way produced , and do not meet , are [ by def . 35. ] parallel to one another . Therefore A B is parallel ...
Página 34
... meet : Therefore the right lines A B , C D infinitely produced , will meet one another ; but they do not meet , fince they are supposed to be parallel . Therefore the angle AGH is not unequal to the angle GHD . It is therefore equal to ...
... meet : Therefore the right lines A B , C D infinitely produced , will meet one another ; but they do not meet , fince they are supposed to be parallel . Therefore the angle AGH is not unequal to the angle GHD . It is therefore equal to ...
Página 35
... meet together . For , if poffible , let them meet in the point L ; therefore B D being cut in half in K the line K в 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 ...
... meet together . For , if poffible , let them meet in the point L ; therefore B D being cut in half in K the line K в 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 ...
Página 48
... meet one another . Let them be produced [ by poft . 2. ] meeting at K , and thro ' K draw [ by prop . 31. ] KL , parallel to E A or F H. And continue out A H , G B to the points L , M. Then is HLKF a parallelogram , whofe diameter is HK ...
... meet one another . Let them be produced [ by poft . 2. ] meeting at K , and thro ' K draw [ by prop . 31. ] KL , parallel to E A or F H. And continue out A H , G B to the points L , M. Then is HLKF a parallelogram , whofe diameter is HK ...
Página 53
... meet CE continued at G. Join C H , G H. Then because the vertical angles A EC , GEB [ by 15 : 1. ] are equal to one another , and the angle DEB [ by fuppofition ] is equal to the angle A E C ; therefore the angles D E B , GEB are equal ...
... meet CE continued at G. Join C H , G H. Then because the vertical angles A EC , GEB [ by 15 : 1. ] are equal to one another , and the angle DEB [ by fuppofition ] is equal to the angle A E C ; therefore the angles D E B , GEB are equal ...
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...