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 1
... greater propriety , as the labours of commentators , besides their dulness , seldom or never answer the expectations of the public in other respects ; which they no doubt are apt to imagine the author himself could have fully gratified ...
... greater propriety , as the labours of commentators , besides their dulness , seldom or never answer the expectations of the public in other respects ; which they no doubt are apt to imagine the author himself could have fully gratified ...
Página 6
... greater . And thus we are to proceed untill we have fatisfied ourselves that thefe common notions are true at least of such straight lines as we can draw upon a piece of paper . I beg the reader's pardon for my impertinence ; but he is ...
... greater . And thus we are to proceed untill we have fatisfied ourselves that thefe common notions are true at least of such straight lines as we can draw upon a piece of paper . I beg the reader's pardon for my impertinence ; but he is ...
Página 15
... greater or lefs than this . The reader has been very inattentive to my directions upon this head , if he does not perceive , that there is an unlimited variety both of acute and obtufe angles , but that there is but one right angle ...
... greater or lefs than this . The reader has been very inattentive to my directions upon this head , if he does not perceive , that there is an unlimited variety both of acute and obtufe angles , but that there is but one right angle ...
Página 31
... greater equal to the lefs . The fimpleft cafe of this propofition would be , when both the lines are drawn from the fame point : for making that point the center , and the shorter line the radius , the circle so described would solve ...
... greater equal to the lefs . The fimpleft cafe of this propofition would be , when both the lines are drawn from the fame point : for making that point the center , and the shorter line the radius , the circle so described would solve ...
Página 47
... greater than AC ; therefore it is not greater . And I appeal to any one , whether the demonftration is either difficult , obfcure or inconclufive when it is confidered in this manner . Nothing can be so senseless as the objections ...
... greater than AC ; therefore it is not greater . And I appeal to any one , whether the demonftration is either difficult , obfcure or inconclufive when it is confidered in this manner . Nothing can be so senseless as the objections ...
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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...