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 |
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Σελίδα 21
... BC , and CD is common , and △ ACD = △ BCD , : . AD = BD ; .. AB is bisected in D. I. 1 . I. 9 I. 4 . Q. E. F. Ex . 1. The straight line , drawn to bisect the vertical angle of an isosceles triangle , also bisects the base . Ex . 2 ...
... BC , and CD is common , and △ ACD = △ BCD , : . AD = BD ; .. AB is bisected in D. I. 1 . I. 9 I. 4 . Q. E. F. Ex . 1. The straight line , drawn to bisect the vertical angle of an isosceles triangle , also bisects the base . Ex . 2 ...
Σελίδα 24
... BC and to the right of it . ( B ) below the line BC and to the left of it . 2. Divide a given angle into four equal parts . 3. The angles B , C , at the base of an isosceles triangle , are bisected by the straight lines BD , CD ...
... BC and to the right of it . ( B ) below the line BC and to the left of it . 2. Divide a given angle into four equal parts . 3. The angles B , C , at the base of an isosceles triangle , are bisected by the straight lines BD , CD ...
Σελίδα 32
... BC , the base of an isosceles triangle BAC , is pro- duced to any point D ; shew that AD is greater than AB . Ex . 3. The perpendicular is the shortest straight line , which can be drawn from a given point to a given straight line ...
... BC , the base of an isosceles triangle BAC , is pro- duced to any point D ; shew that AD is greater than AB . Ex . 3. The perpendicular is the shortest straight line , which can be drawn from a given point to a given straight line ...
Σελίδα 37
... base , is less than the greater of the two sides , or than either , if they be equal . B In the △ ABC , let the side AC be not less than AB . Take any pt . D in BC , and join AD . Then must AD be less than AC . For AC is not less ...
... base , is less than the greater of the two sides , or than either , if they be equal . B In the △ ABC , let the side AC be not less than AB . Take any pt . D in BC , and join AD . Then must AD be less than AC . For AC is not less ...
Σελίδα 38
... base of that which has the greater angle must be greater than the base of the other . D B E G F In the As ABC , DEF , let AB = DE and AC = DF , and let BAC be greater than △ EDF . Then must BC be greater than EF . Of the two sides DE ...
... base of that which has the greater angle must be greater than the base of the other . D B E G F In the As ABC , DEF , let AB = DE and AC = DF , and let BAC be greater than △ EDF . Then must BC be greater than EF . Of the two sides DE ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AB=DE ABCD AC=DF angles equal angular points base BC BC=EF centre chord circumference coincide described diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given circle given line given point given straight line greater than nB 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 plane polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained reflex angle rhombus right angles segment shew shewn square subtended sum of sqq tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 168 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 40 - 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. either the sides adjacent to the equal...
Σελίδα 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Σελίδα 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.
Σελίδα 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.
Σελίδα 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Σελίδα 285 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 91 - In every triangle, the square of the side subtending either 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.