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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Σελίδα 8
... given points , either on contrary sides , or both on the same side of the given line , and in the same plane with it ... circle cannot cut a straight line in more points than two . PROP . XVII . ( VII . ) The perpendicular ( 8 ) APPENDIX I.
... given points , either on contrary sides , or both on the same side of the given line , and in the same plane with it ... circle cannot cut a straight line in more points than two . PROP . XVII . ( VII . ) The perpendicular ( 8 ) APPENDIX I.
Σελίδα 39
... given point , within a given circle , to draw two equal chords , making with one another an angle equal to a given rectilineal angle . PROP . XVI . ( VI . ) If the diameters of two circles are in the same straight line , and have a ...
... given point , within a given circle , to draw two equal chords , making with one another an angle equal to a given rectilineal angle . PROP . XVI . ( VI . ) If the diameters of two circles are in the same straight line , and have a ...
Σελίδα 40
... circle which shall have a given radius , and its center in a given straight line , and shall also touch another straight line , inclined at a given angle to the former . ( IX . ) To describe a circle , the circumference of which shall ...
... circle which shall have a given radius , and its center in a given straight line , and shall also touch another straight line , inclined at a given angle to the former . ( IX . ) To describe a circle , the circumference of which shall ...
Σελίδα 41
... given circle , and each also passing through a given point without that circle : The given straight line being greater than the shortest distance , between the given point and the circumference of the given circle . PROP . XVII . ( xv ...
... given circle , and each also passing through a given point without that circle : The given straight line being greater than the shortest distance , between the given point and the circumference of the given circle . PROP . XVII . ( xv ...
Σελίδα 42
... circle shall be equal to a given finite straight line , which is less than the diameter . ( XVII . ) To draw a tangent to a given circle , such that it's segment , contained between the point of contact , and an indefinite straight line ...
... circle shall be equal to a given finite straight line , which is less than the diameter . ( XVII . ) To draw a tangent to a given circle , such that it's segment , contained between the point of contact , and an indefinite straight line ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... Daniel Cresswell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... D. Cresswell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... D 1776-1844 Cresswell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
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.