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 5
... fame time feveral ftraight lines from the center to the circumference . He is next to fatisfy himfelf of the equality of these ftraight lines , by measuring them with his compaffes his conclufion will be , that they are equal ; and he ...
... fame time feveral ftraight lines from the center to the circumference . He is next to fatisfy himfelf of the equality of these ftraight lines , by measuring them with his compaffes his conclufion will be , that they are equal ; and he ...
Página 7
... fame piece of wood ; and this will illuftrate the fecond and third ; according as you confider one of them as taken away from the whole angle made up of the two ; or as added together to make one . But it will be neceffary previous to ...
... fame piece of wood ; and this will illuftrate the fecond and third ; according as you confider one of them as taken away from the whole angle made up of the two ; or as added together to make one . But it will be neceffary previous to ...
Página 13
... fame time to discover , that the fame ingenious fubtilties would also apply to lines and furfaces , by which means they might likewise be entitled to a place among the incomprehenfibles . I fhall therefore beg leave to call his ...
... fame time to discover , that the fame ingenious fubtilties would also apply to lines and furfaces , by which means they might likewise be entitled to a place among the incomprehenfibles . I fhall therefore beg leave to call his ...
Página 15
... fame time , through the other , at fome distance from its extremity , fo that the one of the pens may make two angles with the other , on each fide one . Turn the pens into the fame direction , and making one of them revolve , and then ...
... fame time , through the other , at fome distance from its extremity , fo that the one of the pens may make two angles with the other , on each fide one . Turn the pens into the fame direction , and making one of them revolve , and then ...
Página 18
... fame order , with a certainty that they are both thinking of the fame thing at the fame time . The art of logic is an inftrument of this kind , but the great . diverfity of opinions prevailing among mankind is a fufficient proof that ...
... fame order , with a certainty that they are both thinking of the fame thing at the fame time . The art of logic is an inftrument of this kind , but the great . diverfity of opinions prevailing among mankind is a fufficient proof that ...
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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...