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

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Versor of. amp

. tr Ratio of circumference to diameter. "log Logarithm of, to base b. logs

Logarithm of, to modulus k. sink, Sine, cosine, etc., to modulus k. COSk, o y y y Jo

Limit of ...

Versor of. amp

**Amplitude**of (argument of). ln Natural logarithm of. e Natural base. tr Ratio of circumference to diameter. "log Logarithm of, to base b. logs

Logarithm of, to modulus k. sink, Sine, cosine, etc., to modulus k. COSk, o y y y Jo

Limit of ...

67 ÆäÀÌÁö

Its length, taken positively, is called the sensor o the magnitude, and the arc-ratio

of the angle it makes with the real axis is called its

Classified and defined with respect to

...

Its length, taken positively, is called the sensor o the magnitude, and the arc-ratio

of the angle it makes with the real axis is called its

**amplitude**(or argument). .Classified and defined with respect to

**amplitude**, the magnitudes themselves are:...

70 ÆäÀÌÁö

The geometric product of two magnitudes a, so, is defined as a third magnitude y,

whose tensor is the algebraic product of the tensors of the factors and whose

The geometric product of two magnitudes a, so, is defined as a third magnitude y,

whose tensor is the algebraic product of the tensors of the factors and whose

**amplitude**is the algebraic sum of their**amplitudes**, constructed by the rules for ... 71 ÆäÀÌÁö

This versor factor is wholly determined by its

frequently useful to express it. For this purpose let i be the versor whose

This versor factor is wholly determined by its

**amplitude**, in terms of which it isfrequently useful to express it. For this purpose let i be the versor whose

**amplitude**is rs2, 6 the**amplitude**of the complex unit so, OX the real axis, B// the ... 72 ÆäÀÌÁö

Show that the ratio of two complex quantities having the same

complex quantities having

quantity.

Show that the ratio of two complex quantities having the same

**amplitude**, or**amplitudes**that differ by + 27, is a real quantity. (7). Show that the ratio of twocomplex quantities having

**amplitudes**that differ by + 4t is a purely imaginaryquantity.

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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