Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith1878 |
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Αποτελέσματα 1 - 5 από τα 66.
Σελίδα 7
... described from any centre at any distance from that centre . IV . That all right angles are equal to one another . V. That two straight lines cannot enclose a space . VI . That if a straight line meet two other straight lines , so as to ...
... described from any centre at any distance from that centre . IV . That all right angles are equal to one another . V. That two straight lines cannot enclose a space . VI . That if a straight line meet two other straight lines , so as to ...
Σελίδα 10
... . 13 . Now AC , BC are each = AB , .. AC = BC . Ax . 1 . Thus AC , AB , BC are all equal , and an equilat . △ ABC has been described on AB . Q. E. F. PROPOSITION II . PROBLEM . From a given point to 10 [ Book I. EUCLID'S ELEMENTS .
... . 13 . Now AC , BC are each = AB , .. AC = BC . Ax . 1 . Thus AC , AB , BC are all equal , and an equilat . △ ABC has been described on AB . Q. E. F. PROPOSITION II . PROBLEM . From a given point to 10 [ Book I. EUCLID'S ELEMENTS .
Σελίδα 12
... described on AB . 2. By a similar construction to that in Prop . I .. describe on a given straight line an isosceles triangle , whose equal sides shall be each equal to another given straight line . 3. Draw a figure for the case in Prop ...
... described on AB . 2. By a similar construction to that in Prop . I .. describe on a given straight line an isosceles triangle , whose equal sides shall be each equal to another given straight line . 3. Draw a figure for the case in Prop ...
Σελίδα 20
... described with its vertex towards the given angle ; shew that there is one case in which the construction will fail , and two in which it will hold good . NOTE . The line dividing an angle into two equal parts is called the B of the ...
... described with its vertex towards the given angle ; shew that there is one case in which the construction will fail , and two in which it will hold good . NOTE . The line dividing an angle into two equal parts is called the B of the ...
Σελίδα 24
... described with centre A and distance AB in D ; and from AD , AE is cut off = AC : shew that AEB is a right angle . PROPOSITION XIII . THEOREM . The angles which one straight 24 [ Book I. EUCLID'S ELEMENTS . EUCLID'S PROPOSITIONS IX TO ...
... described with centre A and distance AB in D ; and from AD , AE is cut off = AC : shew that AEB is a right angle . PROPOSITION XIII . THEOREM . The angles which one straight 24 [ Book I. EUCLID'S ELEMENTS . EUCLID'S PROPOSITIONS IX TO ...
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 equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given circle given point given st given straight line greater Hence inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram perpendicular plane polygon PROBLEM produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained rectilinear figure reflex angle regular pentagon required to describe rhombus right angles segment semicircle shew shewn 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 5 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
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 84 - 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 165 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
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 159 - 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 67 - The complements of the parallelograms which are about the diameter of any parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC...
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 3 - 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.