Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |
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Σελίδα 136
portionals , as the first is to the third , so is any triangle upon the first to a similar ,
and similarly described triangle upon the second . PROP . XX . THEOR . Similar
polygons may be divided into the same number of similar triangles , having the ...
portionals , as the first is to the third , so is any triangle upon the first to a similar ,
and similarly described triangle upon the second . PROP . XX . THEOR . Similar
polygons may be divided into the same number of similar triangles , having the ...
Σελίδα 138
Therefore , universally , it is manifest , that if three straight lines be proportionals ,
as the first is to the third , so is any reetilineal figure upon the first , to a similar ,
and similarly described rectilineal figure upon the second . CoR . 3. Because all ...
Therefore , universally , it is manifest , that if three straight lines be proportionals ,
as the first is to the third , so is any reetilineal figure upon the first , to a similar ,
and similarly described rectilineal figure upon the second . CoR . 3. Because all ...
Σελίδα 141
to AD , as AE to AG ; and DC to CB , as GF to FE ; and also CD to DA , as FG to
GA : therefore the sides of the parallelo- D grams ABCD , AEFG about the equal
angles are proportionals ; and they are therefore similar to one another ( def . 1. 6
. ) ...
to AD , as AE to AG ; and DC to CB , as GF to FE ; and also CD to DA , as FG to
GA : therefore the sides of the parallelo- D grams ABCD , AEFG about the equal
angles are proportionals ; and they are therefore similar to one another ( def . 1. 6
. ) ...
Σελίδα 190
I. THEOR If two solids be contained by the same number of equal and similar
planes similarly situated , and if the inclination of any two contiguous planes in
the one solid be the same . with the inclination of the two equal , and similarly
situated ...
I. THEOR If two solids be contained by the same number of equal and similar
planes similarly situated , and if the inclination of any two contiguous planes in
the one solid be the same . with the inclination of the two equal , and similarly
situated ...
Σελίδα 316
bounded by the same number of equal and similar planes , which are obviously
unequal , the one being eontained within the other . Simson observes , that
Euclid needed oply to have added , that the equal and similar planes must be
similarly ...
bounded by the same number of equal and similar planes , which are obviously
unequal , the one being eontained within the other . Simson observes , that
Euclid needed oply to have added , that the equal and similar planes must be
similarly ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common contained cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved Q. E. D. PROP radius ratio reason rectangle contained rectilineal figure right angles segment shown sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 125 - 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 39 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Σελίδα 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.
Σελίδα 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Σελίδα 30 - If, from the ends of the 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 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Σελίδα 51 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Σελίδα 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |
| Συγγραφείς | Euclid, John Playfair |
| Επιμελητής | John Playfair |
| Έκδοση | 7 |
| Εκδότης | Marot & Walter, 1826 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Μέγεθος | 320 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |