An Elementary Treatise on the Geometrical and Algebraical Investigation of Maxima and Minima: Being the Substance of a Course of Lectures Delivered Conformably to the Will of Lady Sadler : to which is Added A Selection of Propositions Deducible from Euclid's ElementsJ. Smith, 1817 - 436 σελίδες |
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Αποτελέσματα 1 - 5 από τα 54.
Σελίδα 18
... inscribe a square in a given right - angled isosceles triangle . ( xxxIII . ) To describe a triangle which shall have its three sides , taken together , equal to a given finite straight line , and its three angles equal to three given ...
... inscribe a square in a given right - angled isosceles triangle . ( xxxIII . ) To describe a triangle which shall have its three sides , taken together , equal to a given finite straight line , and its three angles equal to three given ...
Σελίδα 19
... inscribe an equilateral triangle , having one of its angular points upon one of the angular points of the square , and its two remaining angular points one in each of two ad- jacent sides of the square . ( XXXVII . ) If , at the ...
... inscribe an equilateral triangle , having one of its angular points upon one of the angular points of the square , and its two remaining angular points one in each of two ad- jacent sides of the square . ( XXXVII . ) If , at the ...
Σελίδα 42
... the former ; and any two adjacent angles of the circumscribed figure shall be , together , the double of that angle , of the inscribed figure , which lies between them . PROP . XX . ( xx . ) If two ( 42 ) APPENDIX I.
... the former ; and any two adjacent angles of the circumscribed figure shall be , together , the double of that angle , of the inscribed figure , which lies between them . PROP . XX . ( xx . ) If two ( 42 ) APPENDIX I.
Σελίδα 45
... of a given circle , straight lines be drawn to the three angles of an inscribed equilateral triangle , the greatest of them shall be equal to the aggregate of the two less . ( xxx . ) The first , third , fifth APPENDIX I. ( 45 )
... of a given circle , straight lines be drawn to the three angles of an inscribed equilateral triangle , the greatest of them shall be equal to the aggregate of the two less . ( xxx . ) The first , third , fifth APPENDIX I. ( 45 )
Σελίδα 46
... inscribed in a given circle , are together equal to the remaining angles of the figure ; any angle whatever being as- sumed as the first . * ( XXXI . ) To make a trapezium , about which a circle may be described , having its four sides ...
... inscribed in a given circle , are together equal to the remaining angles of the figure ; any angle whatever being as- sumed as the first . * ( XXXI . ) To make a trapezium , about which a circle may be described , having its four sides ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD aggregate Algebra altitude angle equal apparent magnitude base Binomial Theorem bisected chord circumference coefficients Cx² derivative describe a circle diameter divided double draw a straight equal perimeter equation equilateral triangle Euclid Euclid's Elements find a point finite straight line function Geometry given angle given circle given finite straight given point given ratio given straight line given triangle greater ratio greatest hypotenuse inscribed isosceles triangle less Let ABC lines be drawn magnitudes MAXIMA AND MINIMA maximum minimum number of sides parallel parallelepiped parallelogram plane prism produced PROP proposition quadrilateral rectilineal figure rectangle contained regular polygon rhomb right angles right-angled triangle scalene triangle SCHOLIUM sector segment shewn square straight line drawn straight line joining subtended tangent Theorem trapezium triangle ABC variable quantity velocity vertex vertical angle wherefore
Δημοφιλή αποσπάσματα
Σελίδα 81 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 83 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 56 - 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...
Σελίδα 36 - In every triangle, the square of the side subtending any of the acute angles is less than the squares of 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 upon it from the opposite angle, and the acute 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...
Σελίδα 32 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 85 - Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part.
Σελίδα 12 - If two triangles have the three angles of one equal to the three angles of the other, each to each, do you think the two triangles are necessarily alike in every respect ? 5.
Σελίδα 16 - 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.
Σελίδα 154 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 22 - If from the right angle of a right-angled triangle, two straight lines be drawn, one perpendicular to the base, and the other bisecting it, they will contain an angle equal to the difference of the two acute angles of the triangle.