The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With the Elements of Plane Trigonometry, and an Appendix in Four Books : With Notes and IllustrationsLongmans, Green, 1845 - 352 σελίδες |
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Σελίδα vii
... fourth of the circum- ference , what is the magnitude of an angle in the segment ? 6. If a chord of a circular arc , 17 inches in length , be divided into two parts of 8 and 9 inches , respectively , by another chord , what is the ...
... fourth of the circum- ference , what is the magnitude of an angle in the segment ? 6. If a chord of a circular arc , 17 inches in length , be divided into two parts of 8 and 9 inches , respectively , by another chord , what is the ...
Σελίδα viii
... FOURTH BOOK OF EUCLID . 1. If a circle be inscribed in a triangle , and if another triangle be formed by joining the points of contact , each angle of the latter triangle is equal to half the sum of the two angles of the original ...
... FOURTH BOOK OF EUCLID . 1. If a circle be inscribed in a triangle , and if another triangle be formed by joining the points of contact , each angle of the latter triangle is equal to half the sum of the two angles of the original ...
Σελίδα ix
... fourth proportional to 12 , 16 , and 39. Answ . 52 . 7. Find a mean proportional between 24 and 54 . Answ . 36 . EXERCISES ON THE SIXTH BOOK OF EUCLID . 1. If the sides of a triangle be 532 , 684 , and 912 , respectively , what are the ...
... fourth proportional to 12 , 16 , and 39. Answ . 52 . 7. Find a mean proportional between 24 and 54 . Answ . 36 . EXERCISES ON THE SIXTH BOOK OF EUCLID . 1. If the sides of a triangle be 532 , 684 , and 912 , respectively , what are the ...
Σελίδα xi
... fourth and sixth definitions may be illustrated in a similar manner . This will be illustrated by applying the edges of two straight rulers to one another , and turning them in different ways . It will also be rendered clearer by a ...
... fourth and sixth definitions may be illustrated in a similar manner . This will be illustrated by applying the edges of two straight rulers to one another , and turning them in different ways . It will also be rendered clearer by a ...
Σελίδα 7
... fourth , the demonstration .. That is , to describe an equilateral triangle , which shall have given a straight line as one of its sides . The word finite is employed to show that the line is not of unlimited length , but is given in ...
... fourth , the demonstration .. That is , to describe an equilateral triangle , which shall have given a straight line as one of its sides . The word finite is employed to show that the line is not of unlimited length , but is given in ...
Άλλες εκδόσεις - Προβολή όλων
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... James Thomson, gen,James Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained corollary cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB.-To produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol scholium segments semicircle sides similar solid angles square of AC straight line drawn tangent THEOR.-If third triangle ABC trigonometry triplicate ratio vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 130 - 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 45 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 2 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Σελίδα 50 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Σελίδα 38 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 7 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 27 - 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 27 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Σελίδα 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 36 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.