## Uniplanar Algebra: Being Part I of a Prop©¡deutic to the Higher Mathematical Analysis |

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In a product the constituent parts are

this may in turn be a

In a product the constituent parts are

**factors**. The product a X & may also be a**factor**in another product, consisting therefore of three**factors**, as (a X b) X c, andthis may in turn be a

**factor**in a product of four**factors**, and so on. 6. Reciprocals. 25 ÆäÀÌÁö

product as one of its

we write a = j, that is, make AM in Fig. Io coincide with /B, then f : y :: 6: m, that is,

m = }. (Prop. 2.) But by the definition of a product m = j X 5; . . . / ¡¿ 6 = 6, and in ...

product as one of its

**factors**. 7. Idemfactor: Real Unit. If in the proportion f: a : b : mwe write a = j, that is, make AM in Fig. Io coincide with /B, then f : y :: 6: m, that is,

m = }. (Prop. 2.) But by the definition of a product m = j X 5; . . . / ¡¿ 6 = 6, and in ...

27 ÆäÀÌÁö

In Art. 6 it was shown that b = / a implies also a = / 5; hence, from the definition / O

= co follows / co = O. The construction for a product (Art. 5) shows that when one

of its

In Art. 6 it was shown that b = / a implies also a = / 5; hence, from the definition / O

= co follows / co = O. The construction for a product (Art. 5) shows that when one

of its

**factors**becomes o or co, the other remaining finite, the product itself is also ... 30 ÆäÀÌÁö

In the construction of a product any

be laid off in the sense opposite to the one it takes when affected with the positive

sign +, and the constructions involving negative

In the construction of a product any

**factor**affected with the negative sign — mustbe laid off in the sense opposite to the one it takes when affected with the positive

sign +, and the constructions involving negative

**factors**lead to the following ... 31 ÆäÀÌÁö

If both

Draw O/3 = — 5 in the negative, J OA = — a in the negative, O/= j in the positive

sense, M AM parallel to B/, intersecting BO produced in M. Then OM = m is

positive ...

If both

**factors**are affected with the negative sign, the construction is as follows:Draw O/3 = — 5 in the negative, J OA = — a in the negative, O/= j in the positive

sense, M AM parallel to B/, intersecting BO produced in M. Then OM = m is

positive ...

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2-plane addition and subtraction Agenda ALGEBRAIC OPERATION amplitude angle arc-ratio arcs base circular and hyperbolic circular sector commutative law complex quantities construction COROLLARY corresponding cosh cosk cos¨¬ cotk csch defined definition denoted direction distance equal equation Euclid's Elements expm exponential expressed factors formula geometric addition Goniometric Ratios Hence hyperbolic functions Hyperbolic Ratios hyperbolic sector imaginary indeterminate form integers intercept inverse Inverse Functions involution law of involution length logarithmic spiral logarithms log¨¬ metathesis modocyclic modulus natural logarithms negative parallel plane points of division polynomial positive Prop proportion PROPOSITION Prove the following quotient rational numbers real axis real magnitudes real quantities reciprocal represent respectively sech sector sinh sink sink w ſ¨¬ straight line tangent tanh tank tensor tion triangle unit circle zero