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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Page vi
... diagonals from the diagrams and the gnomons from the text . In the Third Book I have deviated with even greater boldness from the precise line of Euclid's method . Thus I have given new proofs of the Pro- positions relating to the ...
... diagonals from the diagrams and the gnomons from the text . In the Third Book I have deviated with even greater boldness from the precise line of Euclid's method . Thus I have given new proofs of the Pro- positions relating to the ...
Page vi
... diagonals from the diagrams and the gnomons from the text . In the Third Book I have deviated with even greater boldness from the precise line of Euclid's method . Thus I have given new proofs of the Pro- positions relating to the ...
... diagonals from the diagrams and the gnomons from the text . In the Third Book I have deviated with even greater boldness from the precise line of Euclid's method . Thus I have given new proofs of the Pro- positions relating to the ...
Page 58
... which two sides only are parallel . XXXII . A DIAGONAL of a four - sided figure is the straight line joining two of the opposite angular points . XXXIII . The ALTITUDE of a Parallelogram is the perpen- 58 [ Book I. EUCLID'S ELEMENTS .
... which two sides only are parallel . XXXII . A DIAGONAL of a four - sided figure is the straight line joining two of the opposite angular points . XXXIII . The ALTITUDE of a Parallelogram is the perpen- 58 [ Book I. EUCLID'S ELEMENTS .
Page 59
... diagonals of a square make with each of the sides an angle equal to half a right angle . 2. If two straight lines ... diagonal drawn from that angular point divides the rhombus into two equilateral triangles . PROPOSITION XXXIV . THEOREM ...
... diagonals of a square make with each of the sides an angle equal to half a right angle . 2. If two straight lines ... diagonal drawn from that angular point divides the rhombus into two equilateral triangles . PROPOSITION XXXIV . THEOREM ...
Page 60
... diagonal bisects it . Let ABDC be a □ , and BC a diagonal of the □ . Then must AB = DC and AC = DB , and and △ BAC = 4 ... diagonals of a rectangle are equal . PROPOSITION XXXV . THEOREM . Parallelograms on the same base 00 [ Book I ...
... diagonal bisects it . Let ABDC be a □ , and BC a diagonal of the □ . Then must AB = DC and AC = DB , and and △ BAC = 4 ... diagonals of a rectangle are equal . PROPOSITION XXXV . THEOREM . Parallelograms on the same base 00 [ Book I ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 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...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 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.