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 Seiten |
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Seite 25
... square , a pa- " rallelogram or oblong fquare , Rhombus or Rhomboeides defcri- " bed definition the 30 , 31 , 32 , and 33. Though their properties are there defined , yet we are not taught how to make them as " yet , and confequently ...
... square , a pa- " rallelogram or oblong fquare , Rhombus or Rhomboeides defcri- " bed definition the 30 , 31 , 32 , and 33. Though their properties are there defined , yet we are not taught how to make them as " yet , and confequently ...
Seite 64
... square BG is only double of the triangle BFC because GAC is a straight line . The reader is also carefully to observe whether the conclusions are general or particular ; because it may so happen that a particular position of lines or ...
... square BG is only double of the triangle BFC because GAC is a straight line . The reader is also carefully to observe whether the conclusions are general or particular ; because it may so happen that a particular position of lines or ...
Seite 84
... square , which is divided into right angled paral- lelograms or fquares by lines drawn parallel to the fides ; and the whole mystery confifts in fettling what these spaces are according to the first definition . For instance , in the ...
... square , which is divided into right angled paral- lelograms or fquares by lines drawn parallel to the fides ; and the whole mystery confifts in fettling what these spaces are according to the first definition . For instance , in the ...
Seite 85
... square of AB : again if from the fquare of AB you take away the rectangle contained by AB and BC ; the remainder is the rectangle contained by AB and AC ; all this is obvious from the infpection of the figure ; but as these confequences ...
... square of AB : again if from the fquare of AB you take away the rectangle contained by AB and BC ; the remainder is the rectangle contained by AB and AC ; all this is obvious from the infpection of the figure ; but as these confequences ...
Seite 86
... square of CD the remainder is the the rectangle contained by AD and DB ; and this square of CD added to the rectangle con- tained by AD and DB makes up the fquare of half the line . And in the fixth propofition if from the fquare of CD ...
... square of CD the remainder is the the rectangle contained by AD and DB ; and this square of CD added to the rectangle con- tained by AD and DB makes up the fquare of half the line . And in the fixth propofition if from the fquare of CD ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 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.
Seite 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.
Seite 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.
Seite 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...