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 4
... alfo below the dignity of our author to affect to disguise them by any forced or unnatural conftruction , to make them wear a more philofophic appearance . But although the twelve common notions which he has felected , are to be ...
... alfo below the dignity of our author to affect to disguise them by any forced or unnatural conftruction , to make them wear a more philofophic appearance . But although the twelve common notions which he has felected , are to be ...
Página 19
... alfo two distinct triangles three fides of the triangle FBC are BF , FC , CB and the three angles BFC , FCB , CBF : and the three fides of the triangle BCG are CG , GB , BC ; and the three angles CGB , GBC , BCG : these triangles have a ...
... alfo two distinct triangles three fides of the triangle FBC are BF , FC , CB and the three angles BFC , FCB , CBF : and the three fides of the triangle BCG are CG , GB , BC ; and the three angles CGB , GBC , BCG : these triangles have a ...
Página 24
... alfo are lines drawn from the center B to the circumference " ACE : Therefore both AC and BC are equal to AB ; but by the " first axiome those which are equal to one other are equal to one " another , therefore AC and BC are alfo equal ...
... alfo are lines drawn from the center B to the circumference " ACE : Therefore both AC and BC are equal to AB ; but by the " first axiome those which are equal to one other are equal to one " another , therefore AC and BC are alfo equal ...
Página 29
... alfo particular . That they are not will appear from this , that no confequence is fuppofed to follow from the ftraight lines having any particular length , nor is any construction undertaken upon that fuppofition ; only that the line ...
... alfo particular . That they are not will appear from this , that no confequence is fuppofed to follow from the ftraight lines having any particular length , nor is any construction undertaken upon that fuppofition ; only that the line ...
Página 31
... alfo join the points A and C instead of the points A and B and repeat the same constructions ; and by pro- ceeding thus you will be able to conquer the prejudice of fenfe and to acquire fomething like a scientific view of the problem ...
... alfo join the points A and C instead of the points A and B and repeat the same constructions ; and by pro- ceeding thus you will be able to conquer the prejudice of fenfe and to acquire fomething like a scientific view of the problem ...
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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...