The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth : the Errors by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored : Also, the Book of Euclid's Data, in Like Manner Corrected : to this Edition are Also Annexed, Elements of Plane and Spherical TrigonometryRobert Desilver, 1821 - 516 sider |
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Resultat 1-5 av 92
Side 8
... perpendicular to it . XI . An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . A figure is ...
... perpendicular to it . XI . An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . A figure is ...
Side 21
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is re- quired to ...
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any length both ways , and let C be a point without it . It is re- quired to ...
Side 61
... perpendicular falls , and the straight line intercepted without the trian- gle between the perpendicular and the obtuse angle . Let ABC be an obtuse angled triangle , having the obtuse an- gle ACB , and from the point A let AD be drawn ...
... perpendicular falls , and the straight line intercepted without the trian- gle between the perpendicular and the obtuse angle . Let ABC be an obtuse angled triangle , having the obtuse an- gle ACB , and from the point A let AD be drawn ...
Side 62
... perpendicular let fall upon it from the opposite angle , and the acute angle . * Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendicular ( 12. 1 ...
... perpendicular let fall upon it from the opposite angle , and the acute angle . * Let ABC be any triangle , and the angle at B one of its acute angles , and upon BC , one of the sides containing it , let fall the perpendicular ( 12. 1 ...
Side 63
... perpendicular to BC ; then is BC the straight line between the perpendi- cular and the acute angle at B ; and it is manifest that the square of AB , BC are equal ( 47. 1. ) to the square of AC and twice the square of BC . There- fore ...
... perpendicular to BC ; then is BC the straight line between the perpendi- cular and the acute angle at B ; and it is manifest that the square of AB , BC are equal ( 47. 1. ) to the square of AC and twice the square of BC . There- fore ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
AC is equal altitude angle ABC angle BAC base BC BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar solid angle solid parallelopipeds sphere spherical angle square of AC straight line AB straight line BC tangent THEOR third triangle ABC vertex wherefore
Populære avsnitt
Side 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Side 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Side 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 53 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 21 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Side 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.