Euclid's Elements of Geometry: The Six First Books. To which are Added, Elements of Plain and Spherical Trigonometry, a System of Conick Sections, Elements of Natural Philosophy, as Far as it Relates to Astronomy, According to the Newtonian System, and Elements of Astronomy: with NotesCushing and Jewett, 1822 - 494 σελίδες |
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Αποτελέσματα 1 - 5 από τα 40.
Σελίδα 107
... secant , between that point , and the point or points , in which it touches or cuts the circle , is equal to the difference of the squares of the radius , and the distance of the same point from the centre of the circle . Cor . 4. Hence ...
... secant , between that point , and the point or points , in which it touches or cuts the circle , is equal to the difference of the squares of the radius , and the distance of the same point from the centre of the circle . Cor . 4. Hence ...
Σελίδα 191
... secant of such complement . Thus KD or CE is the cosine , GH the cotangent , and CH the cosecant , of the arch BD or angle BCD ; being the sine , tangent and secant , of the arch GD or angle GCD , Cor . 1 to these definitions . - The ...
... secant of such complement . Thus KD or CE is the cosine , GH the cotangent , and CH the cosecant , of the arch BD or angle BCD ; being the sine , tangent and secant , of the arch GD or angle GCD , Cor . 1 to these definitions . - The ...
Σελίδα 192
... secant , of any arch or angle , is the sine , tangent or secant of its supple- ment , or complement to a semicircle or two right angles . For it is manifest from these definitions , that the same right lines are the sine , tangent and ...
... secant , of any arch or angle , is the sine , tangent or secant of its supple- ment , or complement to a semicircle or two right angles . For it is manifest from these definitions , that the same right lines are the sine , tangent and ...
Σελίδα 193
... secant . The triangles ADC , AHG are , because of the right angles at D and H , and the common angle at A , equiangular ( 32. 1 Eu . ) , therefore AC is to CD , as AG is to GH [ 4. 6 Eu . ] ; but AC , AG are the radiuses , and CD , GH ...
... secant . The triangles ADC , AHG are , because of the right angles at D and H , and the common angle at A , equiangular ( 32. 1 Eu . ) , therefore AC is to CD , as AG is to GH [ 4. 6 Eu . ] ; but AC , AG are the radiuses , and CD , GH ...
Σελίδα 194
... secant of the same angle . From the centre A , at the distance AB , describe a circle , meeting AC in E ; BC is the tangent , and AC the secant , of the arch BE , or angle EAB [ Def . 8 and 9. Pl . Tr . ] , and the ratio of radius to ...
... secant of the same angle . From the centre A , at the distance AB , describe a circle , meeting AC in E ; BC is the tangent , and AC the secant , of the arch BE , or angle EAB [ Def . 8 and 9. Pl . Tr . ] , and the ratio of radius to ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
angle ACB arch asymptote bisected centre centripetal force circle circumference conical surface conick section described diameter difference directrix distance draw ellipse ellipse or hyperbola equal angles equal Ax equal Cor equal Hyp equiangular Euclid's Elements focus given right line greater half sum inscribed less let fall magnitudes meeting the section opposite hyperbolas opposite sections ordinately applied parabola parallel parallelogram perpendicular plain principal vertex PROB produced PROP proportional proposition quadrant radius rect rectangle right angles right line drawn Scholium secant section or opposite segments semidiameter severally equal shewn sides sine spherical angle square of CB submultiple tangent THEOR triangle ABC vertex whence
Δημοφιλή αποσπάσματα
Σελίδα 40 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 430 - Lastly, if it universally appears, by experiments and astronomical observations, that all bodies about the earth gravitate towards the earth, and that in proportion to the quantity of matter which they severally contain: that the moon likewise, according to the quantity of its matter, gravitates towards the earth; that, on the other hand, our sea gravitates towards the moon; and all the planets mutually one towards another; and the comets in like manner towards the sun...
Σελίδα 13 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Σελίδα 116 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 432 - A stone, whirled about in a sling, endeavors to recede from the hand that turns it; and by that endeavor, distends the sling, and that with so much the greater force, as it is revolved with the greater velocity, and as soon as it is let go, flies away.
Σελίδα 376 - ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Σελίδα 461 - In a parabola, the velocity of a body at any distance from the focus is to the velocity of a body revolving in a circle, at the same distance...
Σελίδα 436 - Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say...
Σελίδα 127 - D, is said to be Compounded of the ratios of the first to the second, of the second to the third, and so on to the last.
Σελίδα 106 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. 5. In like manner, a circle is said to be inscribed...