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 47
... GNOMON , PROP . I. If there be two ftraight lines , and one of them be cut into any number of fegments ; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line and each of the ...
... GNOMON , PROP . I. If there be two ftraight lines , and one of them be cut into any number of fegments ; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line and each of the ...
Page 52
... which is common be added ; therefore the whole AH is equal to DF and DL : but AH is the rectangle con- tained by AD , DB for DH is equal to DB ( by cor . to 4. 2. ) : but : : FD , FD , DL or FDL is called a Gnomon ( 52 THE ELEMENTS.
... which is common be added ; therefore the whole AH is equal to DF and DL : but AH is the rectangle con- tained by AD , DB for DH is equal to DB ( by cor . to 4. 2. ) : but : : FD , FD , DL or FDL is called a Gnomon ( 52 THE ELEMENTS.
Page 53
... Gnomon ( by def . 2. 2. ) ; therefore Book II . the Gnomon FDL is equal to the rectangle contained by AD , DB : Let LG which is common be added ; which ( by Cor . to 4. 2. ) is equal to the square of CD : wherefore the Gnomon FDL and ...
... Gnomon ( by def . 2. 2. ) ; therefore Book II . the Gnomon FDL is equal to the rectangle contained by AD , DB : Let LG which is common be added ; which ( by Cor . to 4. 2. ) is equal to the square of CD : wherefore the Gnomon FDL and ...
Page 54
... Gnomon CMG and the Square LG : but the Gnomon CMG and the Square LG is the whole square CEFD , which is the square of CD : wherefore the rectangle contained by AD , DB together with the square of CB is equal to the square of CD ...
... Gnomon CMG and the Square LG : but the Gnomon CMG and the Square LG is the whole square CEFD , which is the square of CD : wherefore the rectangle contained by AD , DB together with the square of CB is equal to the square of CD ...
Page 55
... Gnomon AKF and the square CK are equal to the rec- tangle contained by AB , BC taken twice : Let HF which is com- mon be added , which is the square of AC : therefore the Gno- mon AKF and the squares CK and HF are the whole square ADEB ...
... Gnomon AKF and the square CK are equal to the rec- tangle contained by AB , BC taken twice : Let HF which is com- mon be added , which is the square of AC : therefore the Gno- mon AKF and the squares CK and HF are the whole square ADEB ...
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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 alſo alſo equal angle ABC angle BAC angle contained angle equal apply itſelf baſe BC is equal Book certainly circle ABC circumference common notion conſequences conſtruction cut in halves demonſtrated deſcribed diſtance drawn equal angles equal ſtraight lines equiangular equilateral equimultiples Euclid exceed fame fides firſt given rectilineal given ſtraight line greater hath inſcribe inſtance inſtruments joined leſs let the ſtraight magnitudes moſt muſt neceſſary obſerve oppoſite parallelogram poſition PROP proportionals propoſition purpoſe reader reaſon alſo rectangle contained rectilineal figure remaining angle right angles ſaid ſame manner ſame multiple ſame ratio ſame reaſon ſay ſcience ſecond ſector ſegment ſenſe ſhall ſhould ſide ſimilar ſome ſquare ſquare of AC ſtand ſtraight line AB straight line BC ſtudent ſubject ſuch ſupp ſuppoſe ſuppoſition taken theſe thoſe tiple triangle ABC 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...