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 Notes |
From inside the book
Results 1-5 of 100
Page 102
... tangent and cutting line , are equal to the angles in the alternate segments . If the cutting line pass through the centre , the angles are equal , being right angles [ 18 and 31. 3 ] . If not , from the contact B , draw BA at right ...
... tangent and cutting line , are equal to the angles in the alternate segments . If the cutting line pass through the centre , the angles are equal , being right angles [ 18 and 31. 3 ] . If not , from the contact B , draw BA at right ...
Page 107
... tangent , drawn from the same point to the circle . Cor . 2. - Two tangents drawn to a circle , from any point without it , are equal . For their squares are equal , being each equal to the same rectangle . Cor . 3. - From this , and ...
... tangent , drawn from the same point to the circle . Cor . 2. - Two tangents drawn to a circle , from any point without it , are equal . For their squares are equal , being each equal to the same rectangle . Cor . 3. - From this , and ...
Page 114
... tangent ( HK ) , drawn through their concourse ( A ) ; the rectangles ( DAB , EAC ) , under their seg- ments , between their concourse ( A ) , and the points , in which they meet the circle again , and the parallel , are equal . H- F L ...
... tangent ( HK ) , drawn through their concourse ( A ) ; the rectangles ( DAB , EAC ) , under their seg- ments , between their concourse ( A ) , and the points , in which they meet the circle again , and the parallel , are equal . H- F L ...
Page 191
... tangent of an arch ( BD or AGD ) , or of its corres- ponding angle ( BCD or ACD ) , is a right line ( BF ) , drawn ... tangent , between the centre and tangent , is called the secant of the same arch or angle . 10. The cosine of any arch ...
... tangent of an arch ( BD or AGD ) , or of its corres- ponding angle ( BCD or ACD ) , is a right line ( BF ) , drawn ... tangent , between the centre and tangent , is called the secant of the same arch or angle . 10. The cosine of any arch ...
Page 192
... tangent or 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 or 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 ...
Other editions - View all
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen No preview available - 2023 |
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen No preview available - 2018 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 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.
Page 116 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.
Page 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...