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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... happen , and natural appearances will keep their regular time ; but the wild beafts of the field are as likely to make a proper use of them , as illiterate favages . And the little atten- tion paid by ignorant men to those very ...
... happen , and natural appearances will keep their regular time ; but the wild beafts of the field are as likely to make a proper use of them , as illiterate favages . And the little atten- tion paid by ignorant men to those very ...
Seite 41
... happen to any two triangles not determined to any parti- cular pofition . Then AB being to DE the point B must apply itself to E , it is impoffible to conceive it to have another fituation , which is very different from faying that as ...
... happen to any two triangles not determined to any parti- cular pofition . Then AB being to DE the point B must apply itself to E , it is impoffible to conceive it to have another fituation , which is very different from faying that as ...
Seite 44
... happen from the construction of the firft triangle : therefore the epithet any could not be so properly applied to the triangle FBC as to ABG . I have recommended to thofe whofe imaginations are flow or inactive , these conftructions ...
... happen from the construction of the firft triangle : therefore the epithet any could not be so properly applied to the triangle FBC as to ABG . I have recommended to thofe whofe imaginations are flow or inactive , these conftructions ...
Seite 45
... happen to take in that particular figure which we reason upon , though this particular po- sition make no part of the fuppofition . The ftudent may convince himself of this , if he read the fourth propofition by the afsistance of the ...
... happen to take in that particular figure which we reason upon , though this particular po- sition make no part of the fuppofition . The ftudent may convince himself of this , if he read the fourth propofition by the afsistance of the ...
Seite 64
... happen that a particular position of lines or points will lead to a conclufion , which will by no means follow if these are changed ; and often if it do hold good it may require fome new steps to come at the conclufion . But it seems ...
... happen that a particular position of lines or points will lead to a conclufion , which will by no means follow if these are changed ; and often if it do hold good it may require fome new steps to come at the conclufion . But it seems ...
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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...