Euclidian Geometry |
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Page 56
... diameter of any parallelogram , are equal to one another . S F N G R H Let FGHK be a , and GK one of its diagonals , and SR , PN □ s about the diagonal . Then FQ , QH , the remainings , which are called complements , shall be equal to ...
... diameter of any parallelogram , are equal to one another . S F N G R H Let FGHK be a , and GK one of its diagonals , and SR , PN □ s about the diagonal . Then FQ , QH , the remainings , which are called complements , shall be equal to ...
Page 100
... diameter . PROPOSITION V. The diameter is the greatest chord of a circle , and of all others that nearer to the centre is greater than the more remote . G F H B Let ACB be a diameter of the AGB , HK , FG chords of which HK is nearer to ...
... diameter . PROPOSITION V. The diameter is the greatest chord of a circle , and of all others that nearer to the centre is greater than the more remote . G F H B Let ACB be a diameter of the AGB , HK , FG chords of which HK is nearer to ...
Page 118
... diameter , chord dividing the and AP a APB into B the segments ABP , AQP . Then shall the in the semi- circle APB be a right ; the in the segment ABP greater than a semicircle < a right ≤ ; and the in the segment AQP less than a ...
... diameter , chord dividing the and AP a APB into B the segments ABP , AQP . Then shall the in the semi- circle APB be a right ; the in the segment ABP greater than a semicircle < a right ≤ ; and the in the segment AQP less than a ...
Page 119
... diameter AD ; join DF . Then AFD is a right angle ; = .. LS FDA , FAD are together a right ; = ¿ T ( III . 16 ) and .. DAT ; ( III . 2 ) i.e. S FAT , FAD together . Take away the common FAD . .. LFDA == L FAT ; = L FDA ; LAQF . ( III ...
... diameter AD ; join DF . Then AFD is a right angle ; = .. LS FDA , FAD are together a right ; = ¿ T ( III . 16 ) and .. DAT ; ( III . 2 ) i.e. S FAT , FAD together . Take away the common FAD . .. LFDA == L FAT ; = L FDA ; LAQF . ( III ...
Page 126
... diameter AB . Then AB shall bisect the Oce . For the may be taken up , inverted and applied to its former position , so that AB may fall upon its former position . F Then will AGB fall upon AFB ; .. arc AGB = arc AFB . COR . To divide ...
... diameter AB . Then AB shall bisect the Oce . For the may be taken up , inverted and applied to its former position , so that AB may fall upon its former position . F Then will AGB fall upon AFB ; .. arc AGB = arc AFB . COR . To divide ...
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Common terms and phrases
Algebra Arithmetic base BEGINNERS Cambridge centre chord Christ's College circumference cloth Conic Sections Crown 8vo Describe a circle diagonals diameter divided ELEMENTARY TREATISE English equiangular equilateral Euclid Examples Extra fcap GEOMETRY given angle given circle given point given straight line Grammar greater H Let Hence inscribed intersecting isosceles triangle John's College Latin Let ABC line bisecting locus magnitudes Mathematical meet Owens College parallel parallelogram perimeter perpendicular plane PROBLEM produced Professor proportional PROPOSITION radius ratio rect rectangle rectangle contained rectilineal figure regular polygon render respectively revised rhombus right angles Schools Second Edition segment Similarly squares on AC straight line joining student tangent THEOREM TRIGONOMETRY twice rectangle twice the squares Uppingham School vertex
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Page 157 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 15 - ... and the principles on which the observations made with these instruments are treated for deduction of the distances and weights of the bo.iits of the Solar System, and of a few stars, omitting all minutiit of Elementary Class- Books — continued. formulcE, and all troublesome details of calculation.