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 |
Αναζήτηση στο βιβλίο
Σελίδα 166
... one of the sides of the triangle DKC , as CE to ED , so is ( 2. 6. ) KH to HD : but KH is equal to BG , and HD to GF ... proportional to two given straight lines . Let AB , AC be the two given straight lines , and let them be placed so ...
... one of the sides of the triangle DKC , as CE to ED , so is ( 2. 6. ) KH to HD : but KH is equal to BG , and HD to GF ... proportional to two given straight lines . Let AB , AC be the two given straight lines , and let them be placed so ...
Σελίδα 167
... joined GH , draw EF parallel ( 31. 1. ) to it through the point E : and because GH is parallel to EF , one of the sides of the triangle DEF , DG is G to GE , as DH to HF ( 2. 6. ) ; but DG is equal to A , GE to B , and DH to C ...
... joined GH , draw EF parallel ( 31. 1. ) to it through the point E : and because GH is parallel to EF , one of the sides of the triangle DEF , DG is G to GE , as DH to HF ( 2. 6. ) ; but DG is equal to A , GE to B , and DH to C ...
Σελίδα 174
... so is EF to BG ; therefore ( 11. 5. ) , as AB to DE , so is EF to BG ; wherefore the sides of the trian- gles ABG , DEF , which are about the equal angles , are recipro- cally proportional : but triangles which have the sides about two ...
... so is EF to BG ; therefore ( 11. 5. ) , as AB to DE , so is EF to BG ; wherefore the sides of the trian- gles ABG , DEF , which are about the equal angles , are recipro- cally proportional : but triangles which have the sides about two ...
Σελίδα 176
... angle ABE to the angle FGL . Therefore as the triangle ABE is to the triangle FGL , so is triangle EBC to triangle LGH , and triangle ECD to triangle LHK : and therefore as one ... sides , are one to another in the duplicate ratio of their ...
... angle ABE to the angle FGL . Therefore as the triangle ABE is to the triangle FGL , so is triangle EBC to triangle LGH , and triangle ECD to triangle LHK : and therefore as one ... sides , are one to another in the duplicate ratio of their ...
Σελίδα 180
... angle ABC is equal to the angle AEF : and each of the angles BCD , EFG is equal to the opposite angle DAB ( 34. 1. ) , and therefore are equal to one another ; wherefore the parallelograms ABCD , AEFG are equiangular ; and because the angle ...
... angle ABC is equal to the angle AEF : and each of the angles BCD , EFG is equal to the opposite angle DAB ( 34. 1. ) , and therefore are equal to one another ; wherefore the parallelograms ABCD , AEFG are equiangular ; and because the angle ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained 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 manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius 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 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.
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 : to ... |
| Συγγραφείς | Euclid, Robert Simson |
| Επιμελητής | Robert Simson |
| Εκδότης | Robert Desilver, 1821 |
| Πρωτότυπο από | η Δημόσια Βιβλιοθήκη της Νέας Υόρκης |
| Ψηφιοποιήθηκε στις | 23 Ιουν. 2006 |
| Μέγεθος | 516 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |