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 8
... apply them to particular instances , he will not be able to tell which is which . The reader is to endeavour next to get fomething like a scientific notion of an angle , by correcting the vulgar notion of an angle , by by which is ...
... apply them to particular instances , he will not be able to tell which is which . The reader is to endeavour next to get fomething like a scientific notion of an angle , by correcting the vulgar notion of an angle , by by which is ...
Página 13
... 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 attention to a method of explanation very different from this , but which ...
... 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 attention to a method of explanation very different from this , but which ...
Página 14
... apply a ruler in all directions from fide to fide ; and finding that it touched the table in every point and in every direction , he would conclude that the furface was even . And now we fhall find that the definition is nothing elfe ...
... apply a ruler in all directions from fide to fide ; and finding that it touched the table in every point and in every direction , he would conclude that the furface was even . And now we fhall find that the definition is nothing elfe ...
Página 36
... apply themselves exactly to one another are equal . It is here faid that AB and DE are equal . What do you understand by this word equal ? Certainly it must mean , that , if the straight lines AB and DE be properly placed , they will apply ...
... apply themselves exactly to one another are equal . It is here faid that AB and DE are equal . What do you understand by this word equal ? Certainly it must mean , that , if the straight lines AB and DE be properly placed , they will apply ...
Página 37
... apply . itself to the other ; because if it did not the two ftraight lines . would inclose a space . Therefore in this figure of ours , if it can be proved that the point B applies itself to E , at the fame time that the point C applies ...
... apply . itself to the other ; because if it did not the two ftraight lines . would inclose a space . Therefore in this figure of ours , if it can be proved that the point B applies itself to E , at the fame time that the point C applies ...
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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...