A Text-book of Geometrical DeductionsLongmans, Green and Company, 1891 |
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Resultat 1-5 av 17
Side
... less than . together with . diminished by . triangle . right angle . parallelogram . square on AB . AB CD " " AB - CD 99 rectangle contained by AB and CD . the difference between AB and CD . CHAPTER I. THEOREMS . § 1. ( Bookwork ...
... less than . together with . diminished by . triangle . right angle . parallelogram . square on AB . AB CD " " AB - CD 99 rectangle contained by AB and CD . the difference between AB and CD . CHAPTER I. THEOREMS . § 1. ( Bookwork ...
Side 12
... less than half the sum of the other two sides . ( A Standard Theorem . ) In △ ABC , let D be the mid - point of BC ; it is re- quired to prove that AD < ( AB + AC ) . Produce AD to E , so that DE = AD . Join EC . [ Construction . In As ...
... less than half the sum of the other two sides . ( A Standard Theorem . ) In △ ABC , let D be the mid - point of BC ; it is re- quired to prove that AD < ( AB + AC ) . Produce AD to E , so that DE = AD . Join EC . [ Construction . In As ...
Side 14
... less than the peri- meter of the triangle . A C Use Ex . 1 for the three medians in turn , add the results , and divide by 2 . ( See note on § 1 , Ex . 4 , as to the use of standard theorems . ) 9. Of the three exterior angles of a ...
... less than the peri- meter of the triangle . A C Use Ex . 1 for the three medians in turn , add the results , and divide by 2 . ( See note on § 1 , Ex . 4 , as to the use of standard theorems . ) 9. Of the three exterior angles of a ...
Side 15
... less than the perimeter . Let P be any point within △ ABC ; it is required to prove that ( 1 ) PA + PB + PC > ( BC + CA + AB ) , ( 2 ) PA + PB + PC < BC + CA + AB . B ( 1 ) In △ PBC , PB + PC > BC . [ Euc . I. 20 . Similarly , PC + PA > ...
... less than the perimeter . Let P be any point within △ ABC ; it is required to prove that ( 1 ) PA + PB + PC > ( BC + CA + AB ) , ( 2 ) PA + PB + PC < BC + CA + AB . B ( 1 ) In △ PBC , PB + PC > BC . [ Euc . I. 20 . Similarly , PC + PA > ...
Side 16
... less than twice the sum of the diagonals . B A A For ( 1 ) use Euc . I. 20 to prove that C AB + BC > AC , BC + CD > BD , etc .; ... 2 ( AB + BC + CD + DA ) > 2 ( AC + BD ) , etc. For ( 2 ) use Euc . I. 20 to show that OA + OB > AB , etc ...
... less than twice the sum of the diagonals . B A A For ( 1 ) use Euc . I. 20 to prove that C AB + BC > AC , BC + CD > BD , etc .; ... 2 ( AB + BC + CD + DA ) > 2 ( AC + BD ) , etc. For ( 2 ) use Euc . I. 20 to show that OA + OB > AB , etc ...
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A Text-book of Geometrical Deductions: Corresponding to Euclid, book ..., Bok 2 James Blaikie Uten tilgangsbegrensning - 1892 |
A Text-book of Geometrical Deductions James Andrew Blaikie,William Thomson Uten tilgangsbegrensning - 1891 |
A Text-Book of Geometrical Deductions: Book I. Corresponding to ..., Bok 1 James Blaikie,W. Thomson Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
26 to show 38 to show ABCD altitude angle equal angular points apply Euc bisectors Bookwork centre Construct a right-angled Construct a triangle Construct an isosceles contained angle convex polygon diagonals Draw a straight drawn parallel equal angles equilateral triangle EUCLID exterior angles Find a point find the locus fixed point given angle given line given point given square given straight line given triangle gonals hypotenuse isosceles triangle joining the mid-points LADC Let ABC line which joins lines be drawn median meet BC method of Ex mid-point of BC opposite angles opposite sides parallel straight lines parallelogram perimeter perpendicular point in BC previous Ex quadrilateral rectangle required to prove respectively equal rhombus right angles right-angled triangle Standard Theorem straight line drawn trapezium triangle required Trisect vertex vertical angle
Populære avsnitt
Side 81 - In every triangle, the square on the side subtending an acute angle is less than the sum of 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 perpendicular let fall on it from the opposite angle, and the acute angle.
Side 27 - If two triangles have two sides of the one equal to two sides of the...
Side 135 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Side 136 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Side 138 - If the square described on one side of a triangle be equal to the sum of the squares described on the other two sides, the angle contained by these two sides is a right angle.
Side 81 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Side 137 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Side 50 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.
Side 137 - ... upon the same side together equal to two right angles; the two straight lines shall be parallel to one another.
Side 135 - The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced the angles on the other side of the base shall be equal to one another.