## The teacher's assistant in the "Course of mathematics adapted to the method of instruction in the American colleges |

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### Common terms and phrases

added angled triangle answer arithmetical axis base bisected body Changing signs circle circumference Clearing of fractions co-efficients Co-tang Completing the square compound cosine Course cube cylinder denominator diameter Diff difference of latitude Dist distance Dividing divisor equal equation Euclid Expanding Extracting the square extremes and means feet find the area find the solidity formula fourth frustum geometrical geometrical progression geometrical series given greater Hence hight hypothenuse inclined plane infinite series Isin length less Let x=the number logarithm magnitude Multiplying extremes natural number belonging ordinale parallel parallelepiped parallelogram perpendicular plane sailing polygon problem proportion quotient radical sign radius ratio rectangle contained rectilineal figure Reduce right angles Secant sector segment sides sine square root Substi Substituting numbers Substituting x's value subtracted surface tables tangent Theorem third tion Transposing and uniting Trig unknown quantity velocity

### 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...