The Elements of Euclid: With Dissertations Intended to Assist and Encourage a Critical Examination of These Elements as the Most Effectual Means of Establishing a Juster Taste Upon Mathematical Subjects Than that which at Present PrevailsPrinted at the Clarendon Press, 1781 - 309 páginas |
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Página 7
... angles , other two equal angles ; which may be done by the affiftance of a different corner of the fame piece of wood ; and this will illuftrate the fecond and third ... equal $ сед equal to the angle ACF : and I DISSERTATION I. 7.
... angles , other two equal angles ; which may be done by the affiftance of a different corner of the fame piece of wood ; and this will illuftrate the fecond and third ... equal $ сед equal to the angle ACF : and I DISSERTATION I. 7.
Página 35
... equal to the two fides DE and DF ; each to each , viz . the fide AB equal to DE ; and the fide AC equal to DF ; and ... angles top , why that epithet remaining ? Why , because only one angle in each triangle being equal by the ...
... equal to the two fides DE and DF ; each to each , viz . the fide AB equal to DE ; and the fide AC equal to DF ; and ... angles top , why that epithet remaining ? Why , because only one angle in each triangle being equal by the ...
Página 38
... angles , contained by the equal fides , equal ; it is required to make the third fide , equal to the third fide ; and the two re- maining angles equal to the two remaining angles , each to each ; namely those under which the equal fides ...
... angles , contained by the equal fides , equal ; it is required to make the third fide , equal to the third fide ; and the two re- maining angles equal to the two remaining angles , each to each ; namely those under which the equal fides ...
Página 39
... equal to DE , and the angle BAC equal to the angle EDF ; but that we are quite in the dark as to AC and DF . When ... angles or inclinations of the lines . * But farther , let us fuppofe , that not only AB is equal to DE and AC to DF and ...
... equal to DE , and the angle BAC equal to the angle EDF ; but that we are quite in the dark as to AC and DF . When ... angles or inclinations of the lines . * But farther , let us fuppofe , that not only AB is equal to DE and AC to DF and ...
Página 45
... equal angles CBG , BCF from the equal angles ABG , ACF ; it has nothing pe- culiar to itself ; every thing else consisting of particular prospects of the fourth propofition . But if any one is defirous to have some kind of reason for ...
... equal angles CBG , BCF from the equal angles ABG , ACF ; it has nothing pe- culiar to itself ; every thing else consisting of particular prospects of the fourth propofition . But if any one is defirous to have some kind of reason for ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD alfo alſo angle ABC angle BAC angle contained angle equal apply itſelf bafe baſe BC is equal Book certainly circle ABC circumference common notion confequences conft conftruction cut in halves demonftrated deſcribed diſtance drawn equal angles equiangular equilateral equimultiples Euclid exceed faid fame manner fame multiple fame parallels fame ratio fame reaſon fecond fegment fhall fides fimilar fince firſt fome fquare ftraight line BC fuch fuppofe fuppofition given rectilineal given ſtraight line Gnomon greater hath himſelf impoffible infcribed joined lefs leſs let the ftraight magnitudes moſt muſt neceffary parallelogram PROP propofition proportionals purpoſe reader reaſon rectangle contained rectilineal figure remaining angle remaining fides right angles ſame ſay ſhall ſhould ſome ſquare ſtraight line AB ſubject ſuch ſuppoſe taken theſe thoſe tiple triangle ABC underſtand uſe Wherefore becauſe
Pasajes populares
Página 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 47 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Página 68 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Página 45 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.
Página 15 - 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 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 88 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Página 42 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Página 109 - Draw two diameters AC, BD of the circle ABCD, at right angles to one another; and through the points A, B. C, D, draw (17.
Página 8 - GB is equal to E, and CK to F ; therefore AB is the same multiple of E, that KH is of F: But AB...