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 5
... circumference . He is next to fatisfy himfelf of the equality of these ftraight lines , by measuring them with his ... circumference ; the parts of the ftraight lines intercepted between the two circumferences are equal ; and will ...
... circumference . He is next to fatisfy himfelf of the equality of these ftraight lines , by measuring them with his ... circumference ; the parts of the ftraight lines intercepted between the two circumferences are equal ; and will ...
Page 23
... circumference ; to which every right line " drawn from a point in the middle , which is called the center , " are equal to one another . But what are we yet the wifer ? How " do we know which of thefe infinite lines we are to draw ? To ...
... circumference ; to which every right line " drawn from a point in the middle , which is called the center , " are equal to one another . But what are we yet the wifer ? How " do we know which of thefe infinite lines we are to draw ? To ...
Page 24
... 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 then of the propofition is the demonstrative " part thereof , namely , to prove ...
... 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 then of the propofition is the demonstrative " part thereof , namely , to prove ...
Page 27
... circumference GKL by " the construction premised . Thirdly that DB is equal to DA , is " clear from the conftruction ; for DBA is an equilateral triangle , " two of whose fides DB and DA are . Now by the third axiom " or common notion ...
... circumference GKL by " the construction premised . Thirdly that DB is equal to DA , is " clear from the conftruction ; for DBA is an equilateral triangle , " two of whose fides DB and DA are . Now by the third axiom " or common notion ...
Page 29
... circumferences of the circles have no breadth , otherwise the point would have parts . Likewife by fuppofing the triangle ABC to be an affignable or determinate mag- nitude implies that the points A , B , C have no magnitude for if they ...
... circumferences of the circles have no breadth , otherwise the point would have parts . Likewife by fuppofing the triangle ABC to be an affignable or determinate mag- nitude implies that the points A , B , C have no magnitude for if they ...
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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...