Easy Introduction to Mathematics, Band 2Barlett & Newman, 1814 |
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Seite 3
... described in the problem , is called the SYNTHESIS , OF SYNTHETICAL DEMONSTRATION of the problem , and frequently the COMPOSITION . 9. When the value of any quantity , which was at first un- known , is found and expressed in known terms ...
... described in the problem , is called the SYNTHESIS , OF SYNTHETICAL DEMONSTRATION of the problem , and frequently the COMPOSITION . 9. When the value of any quantity , which was at first un- known , is found and expressed in known terms ...
Seite 68
... described in the three foregoing articles , is called COMPOUNDING THE PROPORTIONS . 81. If there be any number of quantities , and also as many others , which taken two and two in order are proportionals , namely , the first to the ...
... described in the three foregoing articles , is called COMPOUNDING THE PROPORTIONS . 81. If there be any number of quantities , and also as many others , which taken two and two in order are proportionals , namely , the first to the ...
Seite 151
... described hereafter , ) we find a number nearer than that obtained by trial ; we repeat the process , and thereby ob- tain a number nearer than the last ; again we repeat the pro- cess , and obtain a number still nearer , and so on , to ...
... described hereafter , ) we find a number nearer than that obtained by trial ; we repeat the process , and thereby ob- tain a number nearer than the last ; again we repeat the pro- cess , and obtain a number still nearer , and so on , to ...
Seite 218
... described on the three sides of a right angled triangle , their intersections will form two lunar spaces , the sum of which is equal to the area of the triangle ; the proof of which de- pends on Euclid 47. 1 , 31. 6 , and 2. 12. Proclus ...
... described on the three sides of a right angled triangle , their intersections will form two lunar spaces , the sum of which is equal to the area of the triangle ; the proof of which de- pends on Euclid 47. 1 , 31. 6 , and 2. 12. Proclus ...
Seite 243
... described ; viz . 1. Bow Compasses , a small sort which shut up in a hoop ; their use is to de- scribe the circumferences and arcs of very small circles . B Q with a triangular socket and screw , to receive and PART VIII . 243 ...
... described ; viz . 1. Bow Compasses , a small sort which shut up in a hoop ; their use is to de- scribe the circumferences and arcs of very small circles . B Q with a triangular socket and screw , to receive and PART VIII . 243 ...
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Häufige Begriffe und Wortgruppen
Algebra arithmetical progression axis base bisected called centre chord circle circumference CN² co-sec co-sine co-tan completing the square Conic Sections cube curve diameter distance divided draw EC² equal Euclid Euclid's Elements EXAMPLES.-1 find the numbers former fourth fraction geometrical geometrical progression given equation given ratio greater harmonical mean Hence infinite series inversely last term latter latus rectum less likewise logarithms magnitude method multiplied number of terms odd number parallel parallelogram perpendicular PN² polygon problem Prop proposition Q. E. D. Cor quadrant quotient radius rectangle remainder right angles rule secant shew shewn sides sine solidity straight line substituted subtract tangent theor theorems third triangle unknown quantity VC² versed sine whence wherefore whole numbers x=the
Beliebte Passagen
Seite 280 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Seite 235 - If two triangles have two sides of the one equal to two sides of the...
Seite 247 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 62 - If four magnitudes are proportional, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Seite 353 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Seite 232 - But things which are equal to the same are equal to one another...
Seite 256 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Seite 160 - Take the first term from the second, the second from the third, the third from the fourth, &c. and the remainders will form a new series, called the first order of
Seite 269 - II. Two magnitudes are said to be reciprocally proportional to two others, when one of the first is to one of the other magnitudes as the remaining one of the last two is to the remaining one of the first.
Seite 272 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.