The Elements of Euclid, the parts read in the University of Cambridge [book 1-6 and parts of book 11,12] with geometrical problems, by J.W. Colenso1846 |
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Αποτελέσματα 1 - 5 από τα 67.
Σελίδα 3
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a dia- meter and the part of the circumference it cut off . XIX . A ...
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a dia- meter and the part of the circumference it cut off . XIX . A ...
Σελίδα 34
... diameter bisects them , that is , divides them into two equal parts . N.B. - A parallelogram is a four - sided figure , of which the opposite sides are parallel ; and the diameter is the straight line joining two of its opposite angles ...
... diameter bisects them , that is , divides them into two equal parts . N.B. - A parallelogram is a four - sided figure , of which the opposite sides are parallel ; and the diameter is the straight line joining two of its opposite angles ...
Σελίδα 35
... diameter : the opposite sides and angles of the figure are equal to one another , and the diameter BC bisects it . Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal A C B D to one another ( 1 ...
... diameter : the opposite sides and angles of the figure are equal to one another , and the diameter BC bisects it . Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal A C B D to one another ( 1 ...
Σελίδα 38
... diameter AB bisects it ( 1. 34 ) ; and the triangle DBC is half of the parallelogram DBCF , because the diameter DC bisects it : But the halves of equal things are equal ( Ax . 7 ) ; therefore the triangle ABC is equal to the triangle ...
... diameter AB bisects it ( 1. 34 ) ; and the triangle DBC is half of the parallelogram DBCF , because the diameter DC bisects it : But the halves of equal things are equal ( Ax . 7 ) ; therefore the triangle ABC is equal to the triangle ...
Σελίδα 40
... diameter AC bisects it B ( 1. 34 ) ; Therefore also the parallelogram ABCD is double of the triangle EBC . Wherefore , If a parallelogram & c . Q. E.D. PROP . XLII . PROB . To describe a parallelogram that shall be equal to a given ...
... diameter AC bisects it B ( 1. 34 ) ; Therefore also the parallelogram ABCD is double of the triangle EBC . Wherefore , If a parallelogram & c . Q. E.D. PROP . XLII . PROB . To describe a parallelogram that shall be equal to a given ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid, the Parts Read in the University of Cambridge [Book ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal base BC BC is equal centre chord circle ABC circumference cuts the circle diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given straight line gnomon greater ratio inscribed intersection isosceles triangle less Let ABC Let the straight lines be drawn lines drawn meet multiple opposite angles opposite sides parallel to BC parallelogram pentagon perpendicular plane polygon PROB produced proportionals Q.E.D. PROP rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn square of AC straight line &c straight line AB THEOR touches the circle triangle ABC twice the rectangle Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 42 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 33 - F, which is the common vertex of the triangles: that is », together with four right angles. Therefore all the angles of the figure, together with four right angles are equal to twice as many right angles as the figure has sides.
Σελίδα 62 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 22 - If from the ends of a 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 58 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 146 - ... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon.
Σελίδα 194 - 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 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16.
Σελίδα 69 - 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 of the other part.