Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 60
... passes through the centre ; of those which fall upon the concave circumference , the greatest is that which passes through the centre ; and of the rest that which is nearer to that through the centre is always greater than the more ...
... passes through the centre ; of those which fall upon the concave circumference , the greatest is that which passes through the centre ; and of the rest that which is nearer to that through the centre is always greater than the more ...
Página 62
... pass ( Cor . 1. Th . 3. 3. ) through each of the two cen- tres C and D. But no more than one straight line can be drawn through two points ; hence , the straight line which passes through the centres will bisect the chord at right ...
... pass ( Cor . 1. Th . 3. 3. ) through each of the two cen- tres C and D. But no more than one straight line can be drawn through two points ; hence , the straight line which passes through the centres will bisect the chord at right ...
Página 63
... pass through A. E d B COR . 1. If two circles touch each other internally , the distance be- tween their centre must be equal to the difference of their radii : for the circumferences pass through the same point in the line joining the ...
... pass through A. E d B COR . 1. If two circles touch each other internally , the distance be- tween their centre must be equal to the difference of their radii : for the circumferences pass through the same point in the line joining the ...
Página 64
... pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point A ; and let F be the centre of the circle ABC , and G the centre of ADE ; The straight line which joins the points F , G , shall ...
... pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point A ; and let F be the centre of the circle ABC , and G the centre of ADE ; The straight line which joins the points F , G , shall ...
Página 65
... hence every straight line which passes through two of the points just mentioned , will necessarily pass through the third , and be perpendicular to the chord . PROP . XIV . THEOR . Equal straight lines in 9 OF GEOMETRY . BOOK III . 65.
... hence every straight line which passes through two of the points just mentioned , will necessarily pass through the third , and be perpendicular to the chord . PROP . XIV . THEOR . Equal straight lines in 9 OF GEOMETRY . BOOK III . 65.
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore