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 Seiten |
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Seite 16
... unequal sides . 31. A right - angled triangle , is one , which has one right angle . 32. An obtuse angled triangle , one , which has one obtuse angle . 33. An acute - angled triangle , one , which has three acute angles . 34. Parallel ...
... unequal sides . 31. A right - angled triangle , is one , which has one right angle . 32. An obtuse angled triangle , one , which has one obtuse angle . 33. An acute - angled triangle , one , which has three acute angles . 34. Parallel ...
Seite 17
... unequal , that , which arises from the addition to the greater , being the greater . 5. If from unequals , equals be taken away , the remainders are unequal , that , which arises from the subtraction from the greater , being the greater ...
... unequal , that , which arises from the addition to the greater , being the greater . 5. If from unequals , equals be taken away , the remainders are unequal , that , which arises from the subtraction from the greater , being the greater ...
Seite 20
... unequal right lines ( AB , CD ) being given , to cut off from the greater , a part equal to the less . At either extreme A , of the greater of the given right lines , put AE equal to the less CD [ 2. 1 ] . From the centre A , at the ...
... unequal right lines ( AB , CD ) being given , to cut off from the greater , a part equal to the less . At either extreme A , of the greater of the given right lines , put AE equal to the less CD [ 2. 1 ] . From the centre A , at the ...
Seite 21
... unequal [ Ax . 9 ] , contrary to the supposition ; and because the angles C , F are equal [ Hyp . ] , the right line CB would coincide with FE ; and , because , CB , FE are equal [ Hyp . ] , the point B would coincide with the point E ...
... unequal [ Ax . 9 ] , contrary to the supposition ; and because the angles C , F are equal [ Hyp . ] , the right line CB would coincide with FE ; and , because , CB , FE are equal [ Hyp . ] , the point B would coincide with the point E ...
Seite 22
... unequal , they are therefore equal . Cor . - Hence every equiangular triangle is equilateral . For , whichever side be considered as base , the angles adjacent to it are equal , and therefore the sides opposite to them . PROP . VII ...
... unequal , they are therefore equal . Cor . - Hence every equiangular triangle is equilateral . For , whichever side be considered as base , the angles adjacent to it are equal , and therefore the sides opposite to them . PROP . VII ...
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Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Keine Leseprobe verfügbar - 2023 |
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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...
Seite 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.
Seite 116 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 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.
Seite 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...