Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith |
Inni boken
Resultat 1-5 av 49
Side xi
... PROPOSITIONS XXVI . TO XXIX . Note 4. ON THE SYMMETRICAL PROPERTIES OF THE CIRCLE WITH REGARD TO ITS DIAMETER · 150 • 151 · 153 154 • 155 159 EUCLID'S PROPOSITIONS XXX . TO XXXVII . MISCELLANEOUS EXERCISES ON CONTENTS . xi.
... PROPOSITIONS XXVI . TO XXIX . Note 4. ON THE SYMMETRICAL PROPERTIES OF THE CIRCLE WITH REGARD TO ITS DIAMETER · 150 • 151 · 153 154 • 155 159 EUCLID'S PROPOSITIONS XXX . TO XXXVII . MISCELLANEOUS EXERCISES ON CONTENTS . xi.
Side 5
... Diameter . Hence the radius of a circle is half the diameter . XVI . A SEMICIRCLE is the figure contained by a diameter and the part of the circumference cut off by the diameter . XVII . RECTILINEAR figures are those which are contained ...
... Diameter . Hence the radius of a circle is half the diameter . XVI . A SEMICIRCLE is the figure contained by a diameter and the part of the circumference cut off by the diameter . XVII . RECTILINEAR figures are those which are contained ...
Side 69
... diameter of any parallelogram , are equal to one another . H F F Let ABCD be a , of which BD is a diagonal , and EG , HK the s about BD , that is , through which BD passes , and AF , FC the others , which make up the whole figure ABCD ...
... diameter of any parallelogram , are equal to one another . H F F Let ABCD be a , of which BD is a diagonal , and EG , HK the s about BD , that is , through which BD passes , and AF , FC the others , which make up the whole figure ABCD ...
Side 72
... Prove that a pair of the diagonals of the parallelograms , which are about the diameter of any parallelogram , are parallel to each other . PROPOSITION XLVI . PROBLEM . To describe a square upon 72 1242 [ Book 1 . EUCLID'S ELEMENTS .
... Prove that a pair of the diagonals of the parallelograms , which are about the diameter of any parallelogram , are parallel to each other . PROPOSITION XLVI . PROBLEM . To describe a square upon 72 1242 [ Book 1 . EUCLID'S ELEMENTS .
Side 93
... diameter , by twice the square on the other side about that opposite angle . 5. Produce a given straight line AB to C , so that the rect- angle , contained by the sum and difference of AB and AC , may be equal to a given square . 6 ...
... diameter , by twice the square on the other side about that opposite angle . 5. Produce a given straight line AB to C , so that the rect- angle , contained by the sum and difference of AB and AC , may be equal to a given square . 6 ...
Vanlige uttrykk og setninger
AB=DE ABCD AC=DF angle equal angular points base BC BC=EF centre chord circumference coincide described diagonals diameter divided equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given line given point given st given straight line greater Hence hypotenuse inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram pentagon perpendicular polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained rectilinear figure reflex angle rhombus right angles segment Shew shewn square straight lines drawn sum of sqq Take any pt tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Populære avsnitt
Side 42 - 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.
Side 53 - 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.
Side 17 - 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.
Side 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Side 106 - 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.
Side 178 - 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.
Side 188 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 78 - 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.
Side 91 - 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.
Side 5 - 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.