The Teacher's Assistant in the "Course of Mathematics Adapted to the Method of Instruction in the American Colleges |
From inside the book
Results 6-10 of 35
Page 37
... opposite to the equal angles in each ; then shall the other sides be equal , each to each ; and also the third angle of the one to the third angle of the other . XXVII . If a straight line falling upon two other straight lines makes the ...
... opposite to the equal angles in each ; then shall the other sides be equal , each to each ; and also the third angle of the one to the third angle of the other . XXVII . If a straight line falling upon two other straight lines makes the ...
Page 39
... opposite side produced , the square of the side subtending the obtuse angle is greater than the squares of the sides con- taining the obtuse angle , by twice the rectangle contained by the side upon which , when produced , the ...
... opposite side produced , the square of the side subtending the obtuse angle is greater than the squares of the sides con- taining the obtuse angle , by twice the rectangle contained by the side upon which , when produced , the ...
Page 40
... opposite angle of the triangle . B. The sum of the squares of the diameters of any parallelogram is equal to the sum of the squares of the sides of the paral- lelogram . COR . From this demonstration , it is manifest that the diameters ...
... opposite angle of the triangle . B. The sum of the squares of the diameters of any parallelogram is equal to the sum of the squares of the sides of the paral- lelogram . COR . From this demonstration , it is manifest that the diameters ...
Page 42
... opposite angles of any quadrilateral figure described in a circle , are together equal to two right angles . XXIII . Upon the same straight line , and upon the same side of it , there cannot be two similar segments of circles , not ...
... opposite angles of any quadrilateral figure described in a circle , are together equal to two right angles . XXIII . Upon the same straight line , and upon the same side of it , there cannot be two similar segments of circles , not ...
Page 49
... opposite to the equal angles are homologous sides , that is , are the antecedents or conse quents of the ratios . V. If the sides of two triangles , about each of their angles , be proportiona's , the triangles shall be equiangular ...
... opposite to the equal angles are homologous sides , that is , are the antecedents or conse quents of the ratios . V. If the sides of two triangles , about each of their angles , be proportiona's , the triangles shall be equiangular ...
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Common terms and phrases
added answer arithmetical base body Changing signs circle circumference Clearing of fractions co-efficients Co-secant Co-sine Co-tangent Completing the square cot a cot Course Cube Roots denominator diameter Diff difference of latitude Dist distance Dividing divisor equal equation Euclid Extracting the square extremes and means feet find the angle find the area find the solidity frustum geometrical geometrical progression geometrical series given greater Hence hight hypothenuse inches less Let x=the logarithm magnitude Merid miles Multiplying extremes natural number belonging parallelogram parallelopiped perpendicular plane sailing polygon PROBLEM proportion quotient radius ratio rectangle contained Reduce right angles rods Secant sector segment Sine square root straight line Substi Substituting a's Substituting numbers Substituting y's value subtracted surface tables Tangent Theorem Transposing and uniting Trig 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...