The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 56
... fourth of the vertical angle , and from it a line be drawn perpendicular to the base to meet the opposite side pro- duced , then the part produced , the perpendicular , and the remaining side , will form an equilateral triangle . 53 ...
... fourth of the vertical angle , and from it a line be drawn perpendicular to the base to meet the opposite side pro- duced , then the part produced , the perpendicular , and the remaining side , will form an equilateral triangle . 53 ...
Página 59
... fourth of the triangle ACE ; and , conversely , if BD be such that AD is half of AE , then BD is parallel to CE . 82. If the sides of any quadrilateral be bisected and the points of bisection joined , the included figure is a ...
... fourth of the triangle ACE ; and , conversely , if BD be such that AD is half of AE , then BD is parallel to CE . 82. If the sides of any quadrilateral be bisected and the points of bisection joined , the included figure is a ...
Página 172
... fourth , when , any equimultiples whatever of the first and third being taken , and any whatever of the second and fourth , if the multiple of the first be equal to that of the second , the multiple of the third is also equal to that of ...
... fourth , when , any equimultiples whatever of the first and third being taken , and any whatever of the second and fourth , if the multiple of the first be equal to that of the second , the multiple of the third is also equal to that of ...
Página 173
... fourth , and the third is said to have to the fourth a less ratio than the first has to the second . VIII . Analogy , or proportion , is the similitude of ratios . IX . Proportion consists in three terms at least . x . When three ...
... fourth , and the third is said to have to the fourth a less ratio than the first has to the second . VIII . Analogy , or proportion , is the similitude of ratios . IX . Proportion consists in three terms at least . x . When three ...
Página 174
... fourth ; as is shewn in ( 5. 16 ) : XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred that the second is to the first as the fourth to the third ( 5. B ) : xv . Componendo , by composition ; when ...
... fourth ; as is shewn in ( 5. 16 ) : XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred that the second is to the first as the fourth to the third ( 5. B ) : xv . Componendo , by composition ; when ...
Términos y frases comunes
AB² ABCD AC² AD² adjacent angles angle ABC angle ACB angle BAC angle equal base BC BC is equal centre chord circle ABC circumference diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given rectilineal given straight line gnomon hypotenuse inscribed intersection isosceles triangle join less Let ABC lines be drawn lines drawn meet multiple opposite angles parallel to BC parallelogram perpendicular plane polygon PROB produced proportionals Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment semicircle shew shewn square on AC tangents THEOR touches the circle triangle ABC twice the rectangle vertex Wherefore