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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Página vi
... greater boldness from the precise line of Euclid's method . Thus I have given new proofs of the Pro- positions relating to the Contact of Circles : I have used Superposition to prove Propositions 26 to 29 , so as to make each of those ...
... greater boldness from the precise line of Euclid's method . Thus I have given new proofs of the Pro- positions relating to the Contact of Circles : I have used Superposition to prove Propositions 26 to 29 , so as to make each of those ...
Página 4
... greater than a right angle . XI . An ACUTE ANGLE is one which is less than a right angle . B XII . A FIGURE is that which is enclosed by one or more boundaries . XIII . A CIRCLE is a plane figure contained by EUCLID'S ELEMENTS . [ Book ...
... greater than a right angle . XI . An ACUTE ANGLE is one which is less than a right angle . B XII . A FIGURE is that which is enclosed by one or more boundaries . XIII . A CIRCLE is a plane figure contained by EUCLID'S ELEMENTS . [ Book ...
Página 8
... greater than its part . With his Common Notions Euclid takes the ground of authority , saying in effect , " To my Postulates I request , to my Common Notions I claim , your assent . " Euclid develops the science of Geometry in a series ...
... greater than its part . With his Common Notions Euclid takes the ground of authority , saying in effect , " To my Postulates I request , to my Common Notions I claim , your assent . " Euclid develops the science of Geometry in a series ...
Página 11
... remainder AL - remainder BG . Ax . 3 . But BC = BG ; .. AL = BC . Ax . 1 . Thus from pt . A a st . line AL has been drawn = BC . Q. E. F. PROPOSITION III . PROBLEM . From the greater of two Book I. ] II PROPOSITION II .
... remainder AL - remainder BG . Ax . 3 . But BC = BG ; .. AL = BC . Ax . 1 . Thus from pt . A a st . line AL has been drawn = BC . Q. E. F. PROPOSITION III . PROBLEM . From the greater of two Book I. ] II PROPOSITION II .
Página 12
Euclides James Hamblin Smith. PROPOSITION III . PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . D H Ө E Let AB be the greater of the two given st . lines AB , CD . It is required to cut off ...
Euclides James Hamblin Smith. PROPOSITION III . PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . D H Ө E Let AB be the greater of the two given st . lines AB , CD . It is required to cut off ...
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.