The Elements of Euclid: In which the Propositions are Demonstrated in a New and Shorter Manner Than in Former Translations, and the Arrangement of Many of Them Altered, to which are Annexed Plain and Spherical Trigonometry, Tables of Logarithms from 1 to 10,000, and Tables of Sines, Tangents, and Secants, Natural and Artificial |
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Σελίδα 42
Book III . will pass through the point A. If not , let F , G , be the cene ters of the two
circles , and the right line FG joining them j cut the circles in C , D , join FA , AG .
Because F is the a def . 15. 1. center of the circle ABC , FA is equal to FC a ; and ...
Book III . will pass through the point A. If not , let F , G , be the cene ters of the two
circles , and the right line FG joining them j cut the circles in C , D , join FA , AG .
Because F is the a def . 15. 1. center of the circle ABC , FA is equal to FC a ; and ...
Σελίδα 132
Sb . Let these be b Lem . the segments cut off by the right lines EK , KF , FL , LG ,
GM , MH , HN , NE ; then the remaining polygon EKFLGMHN will be greater than
the figure S. Describe the polygon AXBOCPDR , in the circle ABCD , similar to ...
Sb . Let these be b Lem . the segments cut off by the right lines EK , KF , FL , LG ,
GM , MH , HN , NE ; then the remaining polygon EKFLGMHN will be greater than
the figure S. Describe the polygon AXBOCPDR , in the circle ABCD , similar to ...
Σελίδα 140
Then , as the solid Z is to the cone AL , so is the cone EN to some folid less than
the cone AL ; therefore , as the circle EFGH is to the circle BCD , so is the cone
EN to some solid less than the cone AL ; which is impossible ; therefore the circle
...
Then , as the solid Z is to the cone AL , so is the cone EN to some folid less than
the cone AL ; therefore , as the circle EFGH is to the circle BCD , so is the cone
EN to some solid less than the cone AL ; which is impossible ; therefore the circle
...
Σελίδα 144
Book XII PRO P. XVI . PRO B. TWO circles about the same center , to inscribe in
the greater a polygon of equal fides , even in number , that shall not touch the
lefjer circle . a 16. 3 . blem , Let ABCD , EFGH , be two given circles , about the
same ...
Book XII PRO P. XVI . PRO B. TWO circles about the same center , to inscribe in
the greater a polygon of equal fides , even in number , that shall not touch the
lefjer circle . a 16. 3 . blem , Let ABCD , EFGH , be two given circles , about the
same ...
Σελίδα 156
I from the pole of any circle , to its center , a right line be drawn , it will be
perpendicular to the plain of that circle . a def . 26 b 8. I. Let the circle be AFB ,
and its pole C ; from which draw CD to the center , then CD will be perpendicular
to the ...
I from the pole of any circle , to its center , a right line be drawn , it will be
perpendicular to the plain of that circle . a def . 26 b 8. I. Let the circle be AFB ,
and its pole C ; from which draw CD to the center , then CD will be perpendicular
to the ...
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The Elements of Euclid,: In which the Propositions are Demonstrated in a New ... Euclid Προβολή αποσπασμάτων - 1776 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
added altitude angle ABC angle BAC arch baſe becauſe biſect Book XI circle circle ABCD circumference common cone contained cylinder deſcribed diameter difference divided double draw drawn EFGH equal equiangular equimultiples fall fame fides firſt folid fore four fourth given given right line greater half inſcribed join leſs likewiſe magnitudes meet oppoſite parallel parallelogram perpendicular plain polygon priſms produced Prop proportional proved pyramid ratio rectangle remaining right angles right lined figure ſame multiple ſame reaſon Secant ſegment ſides ſimilar Sine ſolid ſphere ſquare taken Tang tangent THEO theſe third touch triangle triangle ABC Wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 80 - 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 72 - F, equal to them in number, be taken two and two in the fame ratio, and if their analogy be perturbate, viz. as A is to B, fo is E to F, and B to C as D to E ; and if the firft A be greater than the third C, then the fourth D will be greater than the fixth F ; if equal, equal ; and, if lefs, lefs.
Σελίδα 91 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Σελίδα x - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles.
Σελίδα 54 - Let ABC be the given circle, and D the given straight line, not greater than the diameter of the circle. It is required to place in the circle ABC a straight line equal to D.
Σελίδα 9 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 13 - From this it is manifest that if one angle of a triangle be equal to the other two it is a right angle, because the angle adjacent to it is equal to the same two ; (i.
Σελίδα 69 - Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many magnitudes in AB equal to C, as there are in...
Σελίδα 91 - BGC: for the same reason, whatever multiple the circumference EN is of the circumference EF, the same multiple is the angle EHN of the angle EHF: and if the circumference BL be equal to the circumference EN, the angle BGL is also equal to the angle EHN ; (in.
Σελίδα 80 - ... reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal, and let the sides DB, BE be placed in the same straight line ; wherefore also FB, BG are in one straight line (2.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The Elements of Euclid: In which the Propositions are Demonstrated in a New and Shorter Manner Than in Former Translations, and the Arrangement of Many of Them Altered, to which are Annexed Plain and Spherical Trigonometry, Tables of Logarithms from 1 to 10,000, and Tables of Sines, Tangents ... |
| Συγγραφέας | Euclid |
| Επιμελητής | George Douglas |
| Εκδότης | author, and sold, 1776 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 8 Ιουν. 2007 |
| Μέγεθος | 264 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |