The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Σελίδα 46
From this proposition it is manifest , that the difference of the squares of two unequal lines AC , CD , is equal to the rectangle contained by their sum AD and difference DB . OF EUCLID . 47 PROP . VI . THEOR . 46 THE ELEMENTS.
From this proposition it is manifest , that the difference of the squares of two unequal lines AC , CD , is equal to the rectangle contained by their sum AD and difference DB . OF EUCLID . 47 PROP . VI . THEOR . 46 THE ELEMENTS.
Σελίδα 288
... that any of the three straight lines must be less than the sum , but greater than the difference of the other two : From this , he shows that the circles must meet one another , in one case ; and says , that it may be proved DM FG H ...
... that any of the three straight lines must be less than the sum , but greater than the difference of the other two : From this , he shows that the circles must meet one another , in one case ; and says , that it may be proved DM FG H ...
Σελίδα 301
... sharpen one's genius to invent others likeit : whereas there is not the least difference between the two demonstrations , except a single word in the construction , which very probably has been owing to an unskilful librarian .
... sharpen one's genius to invent others likeit : whereas there is not the least difference between the two demonstrations , except a single word in the construction , which very probably has been owing to an unskilful librarian .
Σελίδα 315
... merely upon account of two ratios being “ interposed betwixt the extremes , that are equal to one an“ other : So that there is no difference betwixt this compound“ ing of ratios , and the duplication or triplication of them " which ...
... merely upon account of two ratios being “ interposed betwixt the extremes , that are equal to one an“ other : So that there is no difference betwixt this compound“ ing of ratios , and the duplication or triplication of them " which ...
Σελίδα 324
... given straight line AB produced , so as to make the rectangle AN , NB equal to a given space : Or , which is the same thing , Having given AB the difference of the sides of a rectangle , and the magnitude of it , to find the sides .
... given straight line AB produced , so as to make the rectangle AN , NB equal to a given space : Or , which is the same thing , Having given AB the difference of the sides of a rectangle , and the magnitude of it , to find the sides .
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD added altitude angle ABC angle BAC arch base Book Book XI centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter difference divided double draw drawn equal equiangular equimultiples 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 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 47 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.
Σελίδα 306 - 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 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Σελίδα 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Σελίδα 153 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Σελίδα 28 - 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 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.
Σελίδα 5 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Πληροφορίες βιβλιογραφίας
| Τίτλος | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
| Συγγραφέας | Euclid |
| Επιμελητής | Robert Simson |
| Εκδότης | Bell & Bradfute, 1835 |
| Πρωτότυπο από | Πανεπιστήμιο Χάρβαρντ |
| Ψηφιοποιήθηκε στις | 6 Μάιος 2008 |
| Μέγεθος | 513 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |