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 |
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Page 58
... rectangle under two right lines , is that contained by these right lines , or by right lines equal to them , which is equal by Cor . 3. 34. 1 . When a rectangle is denoted by three letters , the middle one is an extreme of both the ...
... rectangle under two right lines , is that contained by these right lines , or by right lines equal to them , which is equal by Cor . 3. 34. 1 . When a rectangle is denoted by three letters , the middle one is an extreme of both the ...
Page 59
... rectangle BH is equal to all its parts the rectangles BK , DL , EH ( Cor . Ax . 8 ) , but , because BG is equal to A ( Constr . ) , the rectangle BH is equal to the rectangle under BC and A ( Cor . 3. 34. 1 ) , and because BG is equal ...
... rectangle BH is equal to all its parts the rectangles BK , DL , EH ( Cor . Ax . 8 ) , but , because BG is equal to A ( Constr . ) , the rectangle BH is equal to the rectangle under BC and A ( Cor . 3. 34. 1 ) , and because BG is equal ...
Page 60
... rectangle under Z and AB , or , which is equal [ Cor . 3. 34. 1 ] , the square of AB , is equal to the rectangles ... rectangle ( CAB ) , under the whole ( AC ) , and one of the parts ( AB ) , is equal to the rectangle ( ABC ) under the ...
... rectangle under Z and AB , or , which is equal [ Cor . 3. 34. 1 ] , the square of AB , is equal to the rectangles ... rectangle ( CAB ) , under the whole ( AC ) , and one of the parts ( AB ) , is equal to the rectangle ( ABC ) under the ...
Page 61
... rectangle under it and their sum , by the rectangle under the same right lines ; as is manifest , by supposing , in both these propositions , the right lines to be AB , BC . PROP . IV . THEOR . If a right line ( AB ) , be cut into any ...
... rectangle under it and their sum , by the rectangle under the same right lines ; as is manifest , by supposing , in both these propositions , the right lines to be AB , BC . PROP . IV . THEOR . If a right line ( AB ) , be cut into any ...
Page 62
... rectangle ACB . Cor . - The square of a right line , is four - fold the square of its half . For , a right line being bisected , the rectangle under the parts , is equal to the square of the half line . PROP . V. THEOR . If a right line ...
... rectangle ACB . Cor . - The square of a right line , is four - fold the square of its half . For , a right line being bisected , the rectangle under the parts , is equal to the square of the half line . PROP . V. THEOR . If a right line ...
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...