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. |
Dentro del libro
Resultados 1-5 de 14
Página xii
... EQUIMULTIPLES - Pp . 211 to 214 . DEFINITIONS I. II . . POSTULATE · METHOD OF NOTATION SCALES OF MULTIPLES AXIOMS . • Note 1 PROPOSITION I. ( EUCL . V. 1 ) · PROPOSITION II . ( EUCL . V. 2 ) . · 211 211 • 211 212 • 212 • 213 • 213 • 214 ...
... EQUIMULTIPLES - Pp . 211 to 214 . DEFINITIONS I. II . . POSTULATE · METHOD OF NOTATION SCALES OF MULTIPLES AXIOMS . • Note 1 PROPOSITION I. ( EUCL . V. 1 ) · PROPOSITION II . ( EUCL . V. 2 ) . · 211 211 • 211 212 • 212 • 213 • 213 • 214 ...
Página 210
... equal in all respects to the original , and that the line joining the centres of the circles , about the two quadrilaterals , bisects PQ . 1872 . iv . 5. A triangle is ... Equimultiples . DEF 210 EUCLID'S ELEMENTS . [ Books I. to IV .
... equal in all respects to the original , and that the line joining the centres of the circles , about the two quadrilaterals , bisects PQ . 1872 . iv . 5. A triangle is ... Equimultiples . DEF 210 EUCLID'S ELEMENTS . [ Books I. to IV .
Página 214
... equimultiples , these must be equimultiples , the one of the second , and the other of the fourth . Let A be the same multiple of B that C is of D ; and let E and F be taken equimultiples of A and C. Then must E and F be equimultiples ...
... equimultiples , these must be equimultiples , the one of the second , and the other of the fourth . Let A be the same multiple of B that C is of D ; and let E and F be taken equimultiples of A and C. Then must E and F be equimultiples ...
Página 217
... equimultiples of the first and third being taken , and any equi- multiples of the second and fourth , if , when the multiple of the first is greater than that of the second , the multiple of the third is greater than that of the fourth ...
... equimultiples of the first and third being taken , and any equi- multiples of the second and fourth , if , when the multiple of the first is greater than that of the second , the multiple of the third is greater than that of the fourth ...
Página 218
... equimultiples of A and C , and nB , nD stand for any equimultiples of B and D : then the Definition may be stated more briefly thus : A is said to have the same ratio to B which C has to D , when mA is found in the same position among ...
... equimultiples of A and C , and nB , nD stand for any equimultiples of B and D : then the Definition may be stated more briefly thus : A is said to have the same ratio to B which C has to D , when mA is found in the same position among ...
Contenido
240 | |
241 | |
242 | |
243 | |
244 | |
255 | |
256 | |
258 | |
57 | |
77 | |
84 | |
93 | |
128 | |
136 | |
159 | |
175 | |
198 | |
211 | |
221 | |
227 | |
233 | |
235 | |
236 | |
237 | |
238 | |
239 | |
259 | |
260 | |
261 | |
262 | |
264 | |
265 | |
274 | |
275 | |
276 | |
278 | |
280 | |
284 | |
290 | |
307 | |
313 | |
334 | |
342 | |
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.