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 51
... bisected by the diagonal AC [ 34. 1 ] , is double the triangle BAC ; 15 D therefore the parallelogram BD is also ... bisect BC in E ( 10. 1 ) , and at the point E , with the right line EC , make the angle CEF equal to the given angle D ...
... bisected by the diagonal AC [ 34. 1 ] , is double the triangle BAC ; 15 D therefore the parallelogram BD is also ... bisect BC in E ( 10. 1 ) , and at the point E , with the right line EC , make the angle CEF equal to the given angle D ...
Page 62
... bisected , the rectangle under the parts , is equal to the square of the half line . PROP . V. THEOR . If a right line ( AB ) , be divided into two equal parts ( AC , CB ) , and two unequal parts ( AD , DB ) ; the rectangle under the ...
... bisected , the rectangle under the parts , is equal to the square of the half line . PROP . V. THEOR . If a right line ( AB ) , be divided into two equal parts ( AC , CB ) , and two unequal parts ( AD , DB ) ; the rectangle under the ...
Page 63
... bisected , as in C ; and , the nearer the point of division is to the middle of the line , the greater the rectangle ... Bisect AB in C. The rectangle AFB with the square of CF , is equal to the square of CB [ 5. 2 ] ; or , which is ...
... bisected , as in C ; and , the nearer the point of division is to the middle of the line , the greater the rectangle ... Bisect AB in C. The rectangle AFB with the square of CF , is equal to the square of CB [ 5. 2 ] ; or , which is ...
Page 64
... bisected , and another right line ( BD ) be added in continuation ; the rectangle ( ADB ) under the whole compound ( AD ) and the part added ( BD ) , with the square of the half line CB ) , is equal to the square of the compound of the ...
... bisected , and another right line ( BD ) be added in continuation ; the rectangle ( ADB ) under the whole compound ( AD ) and the part added ( BD ) , with the square of the half line CB ) , is equal to the square of the compound of the ...
Page 66
... Bisect AB in C , and on CB produced take CE , whose square is equal to the squares of CB and D together ( Cor . 1. 47. 1 ) ; and , since the square of CE is equal to the two squares of CB and D together ( Constr . ) , taking from each ...
... Bisect AB in C , and on CB produced take CE , whose square is equal to the squares of CB and D together ( Cor . 1. 47. 1 ) ; and , since the square of CE is equal to the two squares of CB and D together ( Constr . ) , taking from each ...
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 triangle square of CB submultiple tangent THEOR triangle ABC vertex whence
Popular passages
Page 2 - In conformity to the act of Congress of the United States, entitled, " An act for the encouragement of learning, by securing the copies of maps, charts and books, to the authors and proprietors of such copies, during the times therein mentioned ;
Page 2 - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Page 42 - 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 176 - If two triangles have an angle of one equal to an angle of the other...
Page 118 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 15 - 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 444 - Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.
Page 96 - Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another.
Page 386 - ... 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 49 - Equal triangles on the same base, and on the same side of it, are between the same parallels.