## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method of Instruction in the American Colleges |

### From inside the book

Page 61

Theorem I. In every plane triangle , the sines of the angles are as their opposite sides . Theorem II . In any plane triangte , As the sum of any two of the sides ,

Theorem I. In every plane triangle , the sines of the angles are as their opposite sides . Theorem II . In any plane triangte , As the sum of any two of the sides ,

**to their difference ; so is the tangent of half the sum of the**opposite ...### What people are saying - Write a review

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### Common terms and phrases

added answer arithmetical base becomes belonging body called Changing circle circumference Clearing of fractions Co-secant Co-sine Co-tang common compound contained Course denominator departure described diameter difference Dist distance Dividing drawn equal equation Example Expanding expressed Extracting the square feet Figure find the area forces four fourth geometrical given greater half Hence hight hypothenuse inches latitude leaves length less Let x=the logarithm magnitude method miles multiplied natural number obtained opposite parallel perpendicular places plane polygon PROBLEM proportion quantity quotient radius ratio rectangle Reduce remaining right angles rods rule sailing Secant sector segment side signs similar Sine solidity solution space square root straight line Substituting subtracted surface tables Tangent Theorem third tion Transposing and uniting triangle Trig weight whole

### Popular passages

Page 36 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...

Page 49 - 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.

Page 42 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles...

Page 39 - IF a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 38 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Page 37 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...

Page 38 - Prove it. 6.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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

Page 42 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Page 35 - Upon the same base, and on the same side of it, there cannot be two triangles, that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity, equal to one another.

Page 33 - Then divide the first term of the remainder by the first term of the divisor...