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 37
... because when the point A is upon the point D : and AB upon DE ; it follows from the equality of the angles that AC will take the direction of DF . But if the angles be unequal , although the point A be upon the point D ; and AB upon DE ...
... because when the point A is upon the point D : and AB upon DE ; it follows from the equality of the angles that AC will take the direction of DF . But if the angles be unequal , although the point A be upon the point D ; and AB upon DE ...
Página 38
... because according to the fuppofi- tion , the fides and angles cannot be otherwise than equal . How- ever it is neceffary to fhew that these magnitudes are really equal ; and the suppofition alone is what we must truft to , for bringing ...
... because according to the fuppofi- tion , the fides and angles cannot be otherwise than equal . How- ever it is neceffary to fhew that these magnitudes are really equal ; and the suppofition alone is what we must truft to , for bringing ...
Página 39
... because nothing is faid concerning the angles or inclinations of the lines . * But farther , let us fuppofe , that not only AB is equal to DE and AC to DF and the angle BAC equal to the angle EDF ; but moreover , that AB is equal to AC ...
... because nothing is faid concerning the angles or inclinations of the lines . * But farther , let us fuppofe , that not only AB is equal to DE and AC to DF and the angle BAC equal to the angle EDF ; but moreover , that AB is equal to AC ...
Página 46
... because BC is equal to EF ; and BC applying itself to EF ; alfo BA will apply itself to ED , because the angle ABC is equal to DEF . Certainly for the fame reason CA will apply itself to FD , that is , because the angle ACB is equal to ...
... because BC is equal to EF ; and BC applying itself to EF ; alfo BA will apply itself to ED , because the angle ABC is equal to DEF . Certainly for the fame reason CA will apply itself to FD , that is , because the angle ACB is equal to ...
Página 53
... because the fimpleft cafe of the third , will not be fufficient for cutting off BD equal to AC ; and , what I must beg the reader particularly to attend to , neither can it be done by a ruler and com- paffes ; because there is fomething ...
... because the fimpleft cafe of the third , will not be fufficient for cutting off BD equal to AC ; and , what I must beg the reader particularly to attend to , neither can it be done by a ruler and com- paffes ; because there is fomething ...
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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...