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 83
Side 20
... Shew that ve can prove this Proposition by means of Prop . IV . and PROP . A. , without applying Prop . C. Ex . 2. If the equilateral triangle , employed in the construc- tion , be described with its vertex towards the given angle ; shew ...
... Shew that ve can prove this Proposition by means of Prop . IV . and PROP . A. , without applying Prop . C. Ex . 2. If the equilateral triangle , employed in the construc- tion , be described with its vertex towards the given angle ; shew ...
Side 22
... Shew that in the diagram of Prop . 1x . AF and ED intersect each other at right angles , and that ED is bisected by ... shew that OA , OB , OC are all equal . Ex . 3. Shew that Prop . XI . is a particular case of Prop . IX . PROPOSITION ...
... Shew that in the diagram of Prop . 1x . AF and ED intersect each other at right angles , and that ED is bisected by ... shew that OA , OB , OC are all equal . Ex . 3. Shew that Prop . XI . is a particular case of Prop . IX . PROPOSITION ...
Side 24
... shew that BDC is an isosceles triangle . 4. D , E , F are points taken in the sides BC , CA , AB , of an equilateral triangle , so that BD = CE = AF . Shew that the triangle DEF is equilateral . 5. In a given straight line find a point ...
... shew that BDC is an isosceles triangle . 4. D , E , F are points taken in the sides BC , CA , AB , of an equilateral triangle , so that BD = CE = AF . Shew that the triangle DEF is equilateral . 5. In a given straight line find a point ...
Side 25
... Shew that the angles at O are together equal to four right angles . NOTE ( 1. ) If two angles together make up a right angle , each is called the COMPLEMENT of the other . Thus , in fig . 2 , ABD is the complement of ABE . ( 2. ) If two ...
... Shew that the angles at O are together equal to four right angles . NOTE ( 1. ) If two angles together make up a right angle , each is called the COMPLEMENT of the other . Thus , in fig . 2 , ABD is the complement of ABE . ( 2. ) If two ...
Side 26
... line with BC . .. BD is in the same st . line with BC . Q. E. D. Ex . Shew the necessity of the words the opposite sides in the enunciation . PROPOSITION XV . THEOREM . If two straight lines cut 26 [ Book I. EUCLID'S ELEMENTS .
... line with BC . .. BD is in the same st . line with BC . Q. E. D. Ex . Shew the necessity of the words the opposite sides in the enunciation . PROPOSITION XV . THEOREM . If two straight lines cut 26 [ Book I. EUCLID'S ELEMENTS .
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.