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 σελίδες |
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Σελίδα 3
... Definitions and Demonstrations as they are in the Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppressing others , and mixing his own with Euclid's ...
... Definitions and Demonstrations as they are in the Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppressing others , and mixing his own with Euclid's ...
Σελίδα 4
... definition which Eudoxus or Eu- clid had given of compound ratio , and given an absurd one in place of it in the 5th Definition of the 6th Book , which neither Euclid , Archimedes , Appollonius , nor any geometer before Theon's time ...
... definition which Eudoxus or Eu- clid had given of compound ratio , and given an absurd one in place of it in the 5th Definition of the 6th Book , which neither Euclid , Archimedes , Appollonius , nor any geometer before Theon's time ...
Σελίδα 5
... Definition of this Book depend the 25th and 28th Propositions of it ; and upon the 25th and 26th depend other eight , viz . the 27th , 31st , 32d , 33d , 34th , 36th , 37th , and 40th of the same Book ; and the 12th of the 12th Book ...
... Definition of this Book depend the 25th and 28th Propositions of it ; and upon the 25th and 26th depend other eight , viz . the 27th , 31st , 32d , 33d , 34th , 36th , 37th , and 40th of the same Book ; and the 12th of the 12th Book ...
Σελίδα 6
... a learned gen- tleman . To which are also added , the Elements of Plane and Spherical Trigonometry , which are commonly taught after the Elements of Euclid . 1 THE ELEMENTS OF EUCLID . BOOK I. DEFINITIONS . I. vi PREFACE .
... a learned gen- tleman . To which are also added , the Elements of Plane and Spherical Trigonometry , which are commonly taught after the Elements of Euclid . 1 THE ELEMENTS OF EUCLID . BOOK I. DEFINITIONS . I. vi PREFACE .
Σελίδα 7
... DEFINITIONS . I. A POINT is that which hath no parts , or which hath no mag- nitude . * II . A line is length without breadth . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its ...
... DEFINITIONS . I. A POINT is that which hath no parts , or which hath no mag- nitude . * II . A line is length without breadth . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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...
Σελίδα 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.