Easy Introduction to Mathematics, Band 2Barlett & Newman, 1814 |
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Seite 1
... known , ) understood any thing of the general methods now in use ; accordingly we find but little attempted beyond the solution of nume- rical problems , in the writings of Lucas de Burgo , Cardan , Diophantus , Tar- talea , Bombelli ...
... known , ) understood any thing of the general methods now in use ; accordingly we find but little attempted beyond the solution of nume- rical problems , in the writings of Lucas de Burgo , Cardan , Diophantus , Tar- talea , Bombelli ...
Seite 2
... known or given quantities , and the final letters x , y , z , w , v , & c . to represent unknown quantities , whose values are required to be found . 5. A general algebraic problem is that in which all the quan- tities concerned , both ...
... known or given quantities , and the final letters x , y , z , w , v , & c . to represent unknown quantities , whose values are required to be found . 5. A general algebraic problem is that in which all the quan- tities concerned , both ...
Seite 3
... known , is found and expressed in known terms , the translat- ing of this value out of algebraic into common language , where- in the relation of the quantities concerned is simply declared , is called deducing a THEOREM ' ; but if the ...
... known , is found and expressed in known terms , the translat- ing of this value out of algebraic into common language , where- in the relation of the quantities concerned is simply declared , is called deducing a THEOREM ' ; but if the ...
Seite 13
... known side of the equation ; thus , in the above equation , instead of R2 - 2a - s2 let $ 2 R2 ; whence 4 4 R2 by evolution , x - 2 = ± √ = = = π2 R + S R S + R = -- 2 and y = ( s — x = ) s— 2 s2 2s R + R2 4 S + R 28 - s + R STR ...
... known side of the equation ; thus , in the above equation , instead of R2 - 2a - s2 let $ 2 R2 ; whence 4 4 R2 by evolution , x - 2 = ± √ = = = π2 R + S R S + R = -- 2 and y = ( s — x = ) s— 2 s2 2s R + R2 4 S + R 28 - s + R STR ...
Seite 29
... useful for computing the weight of such bodies as are too large and unwieldy to be moved ; by means of their kind and dimensions , which must be previously known . EXAMPLES . - 1 . A sets out from London PART IV . 29 GENERAL PROBLEMS .
... useful for computing the weight of such bodies as are too large and unwieldy to be moved ; by means of their kind and dimensions , which must be previously known . EXAMPLES . - 1 . A sets out from London PART IV . 29 GENERAL PROBLEMS .
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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.