Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 páginas |
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Página 49
... fore F G and GL are both in the fame right line . And be- cause K F is equal to H G , and parallel to it ; and HG alfo to ML ; KF will be [ by ax . 1. and prop . 30. ] equal and parallel to M L. But the right lines K м , FL join them ...
... fore F G and GL are both in the fame right line . And be- cause K F is equal to H G , and parallel to it ; and HG alfo to ML ; KF will be [ by ax . 1. and prop . 30. ] equal and parallel to M L. But the right lines K м , FL join them ...
Página 52
... fore B A C will be a right angle too . If therefore the fquare which is defcribed upon one fide of a triangle be equal to both the fquares defcribed upon the other two fides , the angle contained by these other two ides will be a right ...
... fore B A C will be a right angle too . If therefore the fquare which is defcribed upon one fide of a triangle be equal to both the fquares defcribed upon the other two fides , the angle contained by these other two ides will be a right ...
Página 64
... , C B E equal . Therefore the angles A B E , E B C will be equal to the angles B E D , FEB ; that is , the whole angle ABC equal to the whole angle FED . Where fore fore fince there are two triangles A B C , 64 Book I ADDITIONS .
... , C B E equal . Therefore the angles A B E , E B C will be equal to the angles B E D , FEB ; that is , the whole angle ABC equal to the whole angle FED . Where fore fore fince there are two triangles A B C , 64 Book I ADDITIONS .
Página 65
... fore will the angle S CAF , BA C be equal to the angles FDC , FDE ; that is , the angle F A B equal to the angle CDE . In like manner the , angles AFD , EFD , as alfo the angles ACD , BCA will be equal ; that is , the angle AFE equal to ...
... fore will the angle S CAF , BA C be equal to the angles FDC , FDE ; that is , the angle F A B equal to the angle CDE . In like manner the , angles AFD , EFD , as alfo the angles ACD , BCA will be equal ; that is , the angle AFE equal to ...
Página 70
... fore becaufe the parallelograms A D , ABIH are [ by 35. 1. ] equal ; fince they ftand upon the fame bafe A B , and are between the fame parallels A B , HD ; and [ by 35. 1. ] the parallelogram A B I H is equal to the parallelogram IL ...
... fore becaufe the parallelograms A D , ABIH are [ by 35. 1. ] equal ; fince they ftand upon the fame bafe A B , and are between the fame parallels A B , HD ; and [ by 35. 1. ] the parallelogram A B I H is equal to the parallelogram IL ...
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...