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 44
It is required to deseribe a parallelogram that shall be equal to the given triangle
ABC , and bave one of its angles equal to D. Bisect ( 10. 1. ) BC in E , join AE ,
and at the point E in the straight line EC make ( 23. 1. ) the angle ĆEF equal to D
...
It is required to deseribe a parallelogram that shall be equal to the given triangle
ABC , and bave one of its angles equal to D. Bisect ( 10. 1. ) BC in E , join AE ,
and at the point E in the straight line EC make ( 23. 1. ) the angle ĆEF equal to D
...
Σελίδα 46
apply the parallelogram GM equal to the triangle DBC , having the angle GHM
equal to the angle E. And because the angle E is equal to each of the angles
FKH , GHM , the angle FKH is equal to GHM ; add to each of these the angle KHG
...
apply the parallelogram GM equal to the triangle DBC , having the angle GHM
equal to the angle E. And because the angle E is equal to each of the angles
FKH , GHM , the angle FKH is equal to GHM ; add to each of these the angle KHG
...
Σελίδα 140
complete the parallelogram DG ; and , taking any straight line K , make ( 12. 6. )
as BC to ... of the ratios of K to L , and L to M ; wherefore also K has to M the ratio
compounded of the ratios of the A sides of the parallelograms . Now , because as
...
complete the parallelogram DG ; and , taking any straight line K , make ( 12. 6. )
as BC to ... of the ratios of K to L , and L to M ; wherefore also K has to M the ratio
compounded of the ratios of the A sides of the parallelograms . Now , because as
...
Σελίδα 142
the parallelogram BE to the parallelogram EF : therefore as the figure ABC is to
the figure KGH , so is the parallelogram BE to the parallelogram EF ( 11.5 . ) : but
the rectilineal figure ABC is equal to the parallelogram BE ; therefore the ...
the parallelogram BE to the parallelogram EF : therefore as the figure ABC is to
the figure KGH , so is the parallelogram BE to the parallelogram EF ( 11.5 . ) : but
the rectilineal figure ABC is equal to the parallelogram BE ; therefore the ...
Σελίδα 306
... harshly , and are , in fact , extremely obscure . The phrase of applying to a
straight line , a parallelogram deficient , or exceeding by another parallelogram ,
is so eliptical , and so little analogous to ordinary language , that there could be
no ...
... harshly , and are , in fact , extremely obscure . The phrase of applying to a
straight line , a parallelogram deficient , or exceeding by another parallelogram ,
is so eliptical , and so little analogous to ordinary language , that there could be
no ...
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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 |