Elements of Arithmetic, Algebra, and GeometryAdam Black and William Tait, 1826 |
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Σελίδα 183
... rectangle contained by AD and DC , we shall simply say , the rectangle AD.DC , placing a point between the two sides of the rectangle . Also , instead of saying the square of any line , for instance of AD , we shall occasionally write ...
... rectangle contained by AD and DC , we shall simply say , the rectangle AD.DC , placing a point between the two sides of the rectangle . Also , instead of saying the square of any line , for instance of AD , we shall occasionally write ...
Σελίδα 184
... rectangle , will express the area or quantity of surface contained in it , as measured by the square described upon the linear unit . Let ABDC be a rectangle , and Ab the linear unit , or unit of length ; then , if AB contain this unit ...
... rectangle , will express the area or quantity of surface contained in it , as measured by the square described upon the linear unit . Let ABDC be a rectangle , and Ab the linear unit , or unit of length ; then , if AB contain this unit ...
Σελίδα 185
... rectangle , & c . Q. E. D. Cor . 1. If a straight line be divided into any two parts , the rectangles contained by ... rectangle contained by the whole , and one of the parts , is equivalent to the rectangle contained by the two parts ...
... rectangle , & c . Q. E. D. Cor . 1. If a straight line be divided into any two parts , the rectangles contained by ... rectangle contained by the whole , and one of the parts , is equivalent to the rectangle contained by the two parts ...
Σελίδα 186
... rectangle contained by the whole , and that part , together with the square of the other part . By the Prop . AB2 = AC2 + CB2 + 2AC.CB , add CB2 to each ; then AR2 + CB2 = AC2 + 2CB2 + 2AC.CB ; but , AC.CB + CB2 = AG + CK AK - AB.BK ...
... rectangle contained by the whole , and that part , together with the square of the other part . By the Prop . AB2 = AC2 + CB2 + 2AC.CB , add CB2 to each ; then AR2 + CB2 = AC2 + 2CB2 + 2AC.CB ; but , AC.CB + CB2 = AG + CK AK - AB.BK ...
Σελίδα 187
... rectangle , & c . Q. E. D. d Cor , 1. If a straight line AB be divided into two equal parts AB , CE , and also into two unequal parts AD , DB ; the rectangle AD.DB , contained by the unequal segments , together with the square of CD ...
... rectangle , & c . Q. E. D. d Cor , 1. If a straight line AB be divided into two equal parts AB , CE , and also into two unequal parts AD , DB ; the rectangle AD.DB , contained by the unequal segments , together with the square of CD ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
algebraic quantities angle ABC angle ACB angle BAC angle CAB angle EBA annex Arithmetic binomial Binomial Theorem bisected Book centre ciphers circumference coefficient consequently continued fraction cube root denominator diameter difference divided dividend divisor drawn equation example expressed exterior angle figure find the values fore fourth given circle given number greater greatest common measure guinea Hence improper fraction join least common multiple less manner merator minuend multiplied number of terms opposite angles parallel parallelogram perpendicular preceding prefixed PROP Q. E. D. Cor quotient ratio Reduce remaining angle Required the sum right angles rule Scholium sides square root straight line subtracted subtrahend surd tangent THEOREM third Transp triangle ABC units unity unknown quantity vulgar fraction Wherefore whole angle whole number
Δημοφιλή αποσπάσματα
Σελίδα 174 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα 132 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 172 - But by the hypothesis, it is less than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at D ; wherefore...
Σελίδα 171 - 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.
Σελίδα 129 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other ; the angle also contained by the sides of that which has the greater base, shall be greater than the angle contained by the sides equal to them of the other.
Σελίδα 171 - C to the remaining angle at F. For, if the angles ABC, DEF be not equal, one of them is greater than the other : Let ABC be the greater, and at the point B, in the straight line AB, make the angle ABG equal to the angle (23.
Σελίδα 164 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square on GEOMETRY.
Σελίδα 142 - EK, because EH is less than EK ; therefore the square of BH is greater than the square of FK, and the straight line BH greater than FK, and therefore BC is greater than FG.
Σελίδα 109 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Σελίδα 148 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two ; and when the adjacent angles are equal, they ate right angles.