Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi. and Xii. of Euclid with Exercises and NotesRivingtons, 1879 - 349 páginas Copy owned by Florence Exton, principle of the college from 1920-1923, when she died unexpectedly in office. |
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Página 26
... Similarly it may be shewn that no other line but BD is in the same st . 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 ...
... Similarly it may be shewn that no other line but BD is in the same st . 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 ...
Página 27
... Similarly it may be shewn that = L AED BEC . Q. E. D. COROLLARY I. From this it is manifest , that if two straight lines cut one another , the four angles , which they make at the point of intersection , are together equal to four right ...
... Similarly it may be shewn that = L AED BEC . Q. E. D. COROLLARY I. From this it is manifest , that if two straight lines cut one another , the four angles , which they make at the point of intersection , are together equal to four right ...
Página 29
... Similarly , if AC be produced to G it may be shewn that and 4 BCG is greater than △ ABC . LBCGL ACD ; .. △ ACD is greater than △ ABC . I. 15 . Q. E. D. Ex . 1. From the same point there cannot be drawn more than two equal straight ...
... Similarly , if AC be produced to G it may be shewn that and 4 BCG is greater than △ ABC . LBCGL ACD ; .. △ ACD is greater than △ ABC . I. 15 . Q. E. D. Ex . 1. From the same point there cannot be drawn more than two equal straight ...
Página 30
... Similarly it may be shewn that s ABC , BAC and also thats BAC , ACB are together less than two rt . 4 s . NOTE 4. On the Sixth Postulate . Q. E. D. We learn from Prop . and CN , which meet in DE in the points O , P , xvII . that if two ...
... Similarly it may be shewn that s ABC , BAC and also thats BAC , ACB are together less than two rt . 4 s . NOTE 4. On the Sixth Postulate . Q. E. D. We learn from Prop . and CN , which meet in DE in the points O , P , xvII . that if two ...
Página 33
... Similarly it may be shewn that AB and BC together are greater than AC , and BC and CA AB . Q. E. D. Ex . 1. Prove that any three sides of a quadrilateral figure are together greater than the fourth side . Ex . 2. Shew that any side of a ...
... Similarly it may be shewn that AB and BC together are greater than AC , and BC and CA AB . Q. E. D. Ex . 1. Prove that any three sides of a quadrilateral figure are together greater than the fourth side . Ex . 2. Shew that any side of a ...
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Términos y frases comunes
AB=DE ABCD AC=DF angles 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 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 plane polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius rectangle contained rectilinear figure reflex angle rhombus right angles segment shew shewn square subtended sum of sqq Take any pt tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Pasajes populares
Página 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.
Página 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.
Página 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...
Página 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...
Página 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Página 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.
Página 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.
Página 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Página 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.
Página 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.