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 sider |
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Resultat 1-5 av 86
Side 13
... taken for granted as obvious or self - evident , is called a postulate . A Theorem , proposes something to be demonstrated , which , when taken for granted as obvious or self - evident , is called an axiom . A Lemma , is something ...
... taken for granted as obvious or self - evident , is called a postulate . A Theorem , proposes something to be demonstrated , which , when taken for granted as obvious or self - evident , is called an axiom . A Lemma , is something ...
Side 17
... taken away , the remainders are equal . 4. If to unequals , equals be added , the wholes are unequal , that , which arises from the addition to the greater , being the greater . 5. If from unequals , equals be taken away , the ...
... taken away , the remainders are equal . 4. If to unequals , equals be added , the wholes are unequal , that , which arises from the addition to the greater , being the greater . 5. If from unequals , equals be taken away , the ...
Side 18
... taken together , not A C H A- B -D C- E B -D equal to the two interior angles ( BGH , GHD ) on the other side of the intersecting right line , taken together ; the right lines ( AB , CD ) , so met by the third , may be so produced ...
... taken together , not A C H A- B -D C- E B -D equal to the two interior angles ( BGH , GHD ) on the other side of the intersecting right line , taken together ; the right lines ( AB , CD ) , so met by the third , may be so produced ...
Side 22
... taken from the equal angles CBD , CAE , the residues CBA , CAB , which are the angles at the base AB , of the triangle ABC , are equal [ Ax . s ] . Corollary . Hence every equilateral triangle is equiangular . For , whichever side be ...
... taken from the equal angles CBD , CAE , the residues CBA , CAB , which are the angles at the base AB , of the triangle ABC , are equal [ Ax . s ] . Corollary . Hence every equilateral triangle is equiangular . For , whichever side be ...
Side 26
... taken on the other side of AB with respect to the given point C , and from the centre C , at the distance CD , let the circle EDF be described ( Post . 3 ) ; which , because the points C , D are on different sides of the right line AB ...
... taken on the other side of AB with respect to the given point C , and from the centre C , at the distance CD , let the circle EDF be described ( Post . 3 ) ; which , because the points C , D are on different sides of the right line AB ...
Andre utgaver - Vis alle
Euclid's Elements of Geometry: The Six First Books. To which are Added ... Rev. John Allen Uten tilgangsbegrensning - 1822 |
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Ingen forhåndsvisning tilgjengelig - 2023 |
Euclid's Elements of Geometry, the First Six Books: To Which Are Added ... John Allen Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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...
Side 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.
Side 116 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 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.
Side 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.
Side 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...
Side 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...
Side 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.
Side 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...