 | Euclid - 1826 - 234 pàgines
...magnitudes be proportional the two extremes shall be greater than double of the mean. EUCLID'S ELEMENTS. BOOK VI. DEFINITIONS. 1. Similar rectilineal figures are those which have their angles equal each to each, and the sides about the equal angles proportional. 2. Reciprocal figures... | |
 | Robert Simson - 1827 - 546 pàgines
...they are very frequently made use of by geometers. THE ELEMENTS OF EUCLID. BOOK VI. DEFINITIONS. I. SIMILAR rectilineal figures are those which have their...and the sides about the equal angles proportionals. II. See N. " Reciprocal figures, viz. triangles and parallelograms, " are such as have their sides... | |
 | John Radford Young - 1827 - 228 pàgines
...sides of two similar figures are those, which are each interjacent to two angles respectively equal. In different circles similar arcs, sectors, and segments,...which the arcs subtend equal angles at the centre. 3. If two sides of another figure form the extremes, and two sides of another figure form the means,... | |
 | John Playfair - 1829 - 210 pàgines
...between them, according as they meet within or without the circle. END OF BOOK IIT. ELEMENTS OF GEOMETRY. BOOK VI. DEFINITIONS. 1. Similar rectilineal figures...each to each, and the sides about the equal angles proportional. A. In similar figures the sides which are opposite to equal angles are homologous or... | |
 | Pierce Morton - 1830 - 584 pàgines
...other. 14. (Eue. vi. Def.}.) Two rectilineal figures are said to be similar when they have all their angles equal, each to each, and the sides about the equal angles proportionals.* (Eue. vi. 21.) It is evident from this definition that rectilineal figures, which are similar to the... | |
 | Euclides - 1834 - 518 pàgines
...use of by geometers. THE ELEMENTS OF EUCLID. BOOK VI. DEFINITIONS. I. SIMILAR rectilineal figures arc those which have their several angles equal, .. each...the sides about the /^ \ equal angles proportionals. See N. II. " Reciprocal figures, viz. triangles and parallelograms, are " such as have their sides... | |
 | Euclid - 1835 - 540 pàgines
...a, b, c, d. THE ELEMENTS OF EUCLID. BOOK VI. DEFINITIONS. I. SIMILAR rectilineal figures are Book VI those which have their several angles equal each to...and the sides about the equal angles proportionals. II. " Reciprocal figures, viz. triangles and parallelograms, are such See N. " as have their sides... | |
 | 1835 - 684 pàgines
...other. 14. (Eue. vi. Def.}.) Two rectilineal figures are said to be similar when they have all their angles equal, each to each, and the sides about the equal angles proportionals.* (Eue. vi. 21.) It is evident from this definition that rectilineal figures, which are similar to the... | |
 | 1836 - 488 pàgines
...two to their difference. F. Ratios which are compounded of equal ratios, are equal to one another. BOOK vi. — DEFINITIONS. 1. Similar rectilineal figures...and the sides about the equal angles proportionals. 2. Two sides of one figure are sakl to be reciprocally proportional to two sides of another, whet)... | |
 | John Playfair - 1836 - 148 pàgines
...IV. When they cannot be so divided, they may be said to be incommeasurable. V. Rectilineal figures which have their several angles equal, each to each, and the sides about the equal angles proportional, differ only in size, and therefore are the same in shape or similar. PROP. I. 'PROBLEM.... | |
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Reciprocal figures, viz. triangles and parallelograms, " are such as have their sides about two of their " angles proportionals in such a manner, that a side 
