Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith1876 - 349 σελίδες |
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Αποτελέσματα 1 - 5 από τα 59.
Σελίδα 25
... Q. E. D. Ex . Straight lines drawn connecting the opposite angular points of a quadrilateral figure intersect each other in O. Shew that the angles at O are together equal to four right angles . NOTE ( 1. ) If two angles together make ...
... Q. E. D. Ex . Straight lines drawn connecting the opposite angular points of a quadrilateral figure intersect each other in O. Shew that the angles at O are together equal to four right angles . NOTE ( 1. ) If two angles together make ...
Σελίδα 26
... Q. E. D. Ex . Shew the necessity of the words the opposite sides in the enunciation . PROPOSITION XV . THEOREM . If two straight lines cut 26 [ Book I. EUCLID'S ELEMENTS .
... Q. E. D. Ex . Shew the necessity of the words the opposite sides in the enunciation . PROPOSITION XV . THEOREM . If two straight lines cut 26 [ Book I. EUCLID'S ELEMENTS .
Σελίδα 27
... Q. E. D. COROLLARY I. From this it is manifest , that if two straight lines cut one another , the four angles ... Ex . 1. Shew that the bisectors of AED and BEC are in the same straight line . Ex . 2. Prove that △ AED is equal to ...
... Q. E. D. COROLLARY I. From this it is manifest , that if two straight lines cut one another , the four angles ... Ex . 1. Shew that the bisectors of AED and BEC are in the same straight line . Ex . 2. Prove that △ AED is equal to ...
Σελίδα 29
... Q. E. D. Ex . 1. From the same point there cannot be drawn more than two equal straight lines to meet a given straight line . Ex . 2. If , from any point , a straight line be drawn to a given straight line making with it an acute and an ...
... Q. E. D. Ex . 1. From the same point there cannot be drawn more than two equal straight lines to meet a given straight line . Ex . 2. If , from any point , a straight line be drawn to a given straight line making with it an acute and an ...
Σελίδα 31
... Q. E. D. Ex . Shew that if two angles of a triangle be equal , the sides which subtend them are equal also ( Eucl . I. 6 ) . PROPOSITION XIX . THEOREM . If one angle of a Book I. ] 31 PROPOSITION XVIII .
... Q. E. D. Ex . Shew that if two angles of a triangle be equal , the sides which subtend them are equal also ( Eucl . I. 6 ) . PROPOSITION XIX . THEOREM . If one angle of a Book I. ] 31 PROPOSITION XVIII .
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, Containing Books I. to Vi.And Portions of Books Xi ... James Hamblin Smith,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2022 |
Elements of Geometry, Containing Books I. to VI.and Portions of Books XI ... James Hamblin Smith,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angles equal angular points base BC BC=EF bisecting the angle centre chord circumference coincide diagonals diameter divided equal angles equal circles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given line given point given st given straight line greater than nD Hence inscribed isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram perpendicular produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius rectangle contained reflex angle required to describe rhombus right angles segment semicircle shew shewn straight line joining subtended sum of sqq tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 51 - 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 38 - 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. either the sides adjacent to the equal...
Σελίδα 178 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon...
Σελίδα 50 - 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 together equal to two right angles.
Σελίδα 104 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Σελίδα 187 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 89 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Σελίδα 5 - 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.
Σελίδα 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.