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 |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 16
Book I. Because the point B is the centre of the circle CGH , BC is equal e to BG ; and because D is the centre of the circle GKL , e 15. Def . DL is equal to DG , and DA , DB , parts of them , are equal ; theref 3.
Book I. Because the point B is the centre of the circle CGH , BC is equal e to BG ; and because D is the centre of the circle GKL , e 15. Def . DL is equal to DG , and DA , DB , parts of them , are equal ; theref 3.
Σελίδα 17
AB to DE , and AC to DF ; A D Book I. and the angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall ...
AB to DE , and AC to DF ; A D Book I. and the angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall ...
Σελίδα 18
等 A Book I. equal to AC , and let the straight lines AB , AC be produced to . D and E , the angle ABC shall be equal to the angle ACB , and . the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off ...
等 A Book I. equal to AC , and let the straight lines AB , AC be produced to . D and E , the angle ABC shall be equal to the angle ACB , and . the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off ...
Σελίδα 19
a Let ABC be a triangle having the angle ABC equal to the Book I. angle ACB ; the side AB is also equal to the side AC . For if AB be not equal to AC , one of them is greater than the other : let AB be the greater , and from it cut a ...
a Let ABC be a triangle having the angle ABC equal to the Book I. angle ACB ; the side AB is also equal to the side AC . For if AB be not equal to AC , one of them is greater than the other : let AB be the greater , and from it cut a ...
Σελίδα 20
But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; thereE fore , because AC is equal to AD in the F triangle ACD , the angles ECD , FDC upon the other side of the base CD are с equal a to ...
But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; thereE fore , because AC is equal to AD in the F triangle ACD , the angles ECD , FDC upon the other side of the base CD are с equal a to ...
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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
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
ABCD added altitude angle ABC angle BAC arch base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 17 - FG; then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this is impossible (i.
Σελίδα 35 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 67 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Σελίδα 92 - IF a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 26 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
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 of the whole and that part.
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 22 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 161 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Σελίδα 21 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Πληροφορίες βιβλιογραφίας
| Τίτλος | 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 |
| Συγγραφέας | Euclid |
| Εκδότης | Conrad and Company, 1810 |
| Πρωτότυπο από | η Δημόσια Βιβλιοθήκη της Νέας Υόρκης |
| Ψηφιοποιήθηκε στις | 21 Ιουν. 2006 |
| Μέγεθος | 518 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |