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 30.
Σελίδα 13
... falls on DE , then . AB = DE , .. B will coincide with E. And AB coincides with DE , and .. AC will fall on DF . BAC ... fall otherwise as EOF : then the two st . lines BC , EF will enclose a space , which is impossible . Post . 5 . Ax ...
... falls on DE , then . AB = DE , .. B will coincide with E. And AB coincides with DE , and .. AC will fall on DF . BAC ... fall otherwise as EOF : then the two st . lines BC , EF will enclose a space , which is impossible . Post . 5 . Ax ...
Σελίδα 14
... fall between ED and EF in the direction EP , ABC is less than DEF . If BA fall in the direction EQ so that ED is between EQ and EF , ABC is greater than DEF . NOTE 2. On the Conditions of Equality of two Triangles 14 [ Book L EUCLID'S ...
... fall between ED and EF in the direction EP , ABC is less than DEF . If BA fall in the direction EQ so that ED is between EQ and EF , ABC is greater than DEF . NOTE 2. On the Conditions of Equality of two Triangles 14 [ Book L EUCLID'S ...
Σελίδα 17
... falls on BC ; then . EF = BC , ... F will coincide with C ; and Again , DEF = 2 ABC , .. ED will fall on BA ; .. D will fall on BA or BA produced . DFE = 2 ACB , .. FD will fall on CA ; .. D will fall on CA or CA produced . .. D must ...
... falls on BC ; then . EF = BC , ... F will coincide with C ; and Again , DEF = 2 ABC , .. ED will fall on BA ; .. D will fall on BA or BA produced . DFE = 2 ACB , .. FD will fall on CA ; .. D will fall on CA or CA produced . .. D must ...
Σελίδα 18
... falls on the side of BC opposite to the side on which A falls ; and join AD . CASE I. When AD passes through BC . B D Then in △ ABD , ::: BD = BA , .. 4 BAD = 4 BDA , I. A. And in ACD , ::: CD = CA , .. △ CAD = 2 CDA , I. A. .. sum of ...
... falls on the side of BC opposite to the side on which A falls ; and join AD . CASE I. When AD passes through BC . B D Then in △ ABD , ::: BD = BA , .. 4 BAD = 4 BDA , I. A. And in ACD , ::: CD = CA , .. △ CAD = 2 CDA , I. A. .. sum of ...
Σελίδα 29
... same point , a perpendicular be drawn to the given line ; the perpendicular will fall on the side of the acute angle . PROPOSITION XVII . THEOREM . Any two angles of a Book I. ] 29 PROPOSITION XVI . EUCLID'S PROPOSITIONS XVI AND XVII.
... same point , a perpendicular be drawn to the given line ; the perpendicular will fall on the side of the acute angle . PROPOSITION XVII . THEOREM . Any two angles of a Book I. ] 29 PROPOSITION XVI . EUCLID'S PROPOSITIONS XVI AND XVII.
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.