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 Prevails |
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Page 6
... fides , being afraid to meddle with circular arches , leaft we should conjure up a prejudice which we might want art afterwards to lay . By the affistance of this triangular piece of wood , make two equal incli- nations ( or angles ) ...
... fides , being afraid to meddle with circular arches , leaft we should conjure up a prejudice which we might want art afterwards to lay . By the affistance of this triangular piece of wood , make two equal incli- nations ( or angles ) ...
Page 18
... fides and three angles ; each of which ought to be particularly attended to . It will be useful alo to obferve ; that the triangles ABG , ACF though they have feveral parts in common , are nevertheless to be confidered as much as ...
... fides and three angles ; each of which ought to be particularly attended to . It will be useful alo to obferve ; that the triangles ABG , ACF though they have feveral parts in common , are nevertheless to be confidered as much as ...
Page 19
... fides of the triangle ABG are AG , AB , BG and the three angles are ABG , AGB , GAB : and of the triangle ACF the three fides are AF , AC , CF ; and the three angles ACF , AFC , CAF and the angle at A or DAE is faid to be common to the ...
... fides of the triangle ABG are AG , AB , BG and the three angles are ABG , AGB , GAB : and of the triangle ACF the three fides are AF , AC , CF ; and the three angles ACF , AFC , CAF and the angle at A or DAE is faid to be common to the ...
Page 22
... fides equal to one another . ' 66 " This first propofition is a problem , which explains a way how- " to do and perform the thing required , as well as fhews how to " manifeft the truth and certainty of the thing done : It contains ...
... fides equal to one another . ' 66 " This first propofition is a problem , which explains a way how- " to do and perform the thing required , as well as fhews how to " manifeft the truth and certainty of the thing done : It contains ...
Page 24
... fides of fome figure ; or of the rays or lines drawn from the center to the circumference of a circle , he chufes rather to " make use of an equilateral triangle to find out that propriety of a point fo pofited . " " The fecond part ...
... fides of fome figure ; or of the rays or lines drawn from the center to the circumference of a circle , he chufes rather to " make use of an equilateral triangle to find out that propriety of a point fo pofited . " " The fecond part ...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid No preview available - 2016 |
Common terms and phrases
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
Popular passages
Page 3 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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...
Page 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.
Page 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.
Page 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.
Page 86 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 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.
Page 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.
Page 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.
Page 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...