Euclid's Elements of plane geometry [book 1-6] with explanatory appendix, and supplementary propositions, by W.D. Cooley1840 |
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Αποτελέσματα 1 - 5 από τα 27.
Σελίδα 23
... fore AC BC ( Ax . 1 ) ; and since AC , AB , and BC are equal to one another , the triangle ABC , constructed upon the given straight line AB , is equilateral . PROP . II . PROB . From a given point ( c ) , to draw a straight line equal ...
... fore AC BC ( Ax . 1 ) ; and since AC , AB , and BC are equal to one another , the triangle ABC , constructed upon the given straight line AB , is equilateral . PROP . II . PROB . From a given point ( c ) , to draw a straight line equal ...
Σελίδα 26
... fore DC cannot be equal to AB : and the same may be de- monstrated of any other part of AC , which is therefore not greater than AB . In like manner AB may be shown to be not greater than AC . Therefore the sides AB and AC sub- tending ...
... fore DC cannot be equal to AB : and the same may be de- monstrated of any other part of AC , which is therefore not greater than AB . In like manner AB may be shown to be not greater than AC . Therefore the sides AB and AC sub- tending ...
Σελίδα 33
... fore greater than the third side BC . COR . - Hence the difference between any two sides of a triangle is less than the third side . For the greater of those two sides is equal to the less side and the difference between them ; but , by ...
... fore greater than the third side BC . COR . - Hence the difference between any two sides of a triangle is less than the third side . For the greater of those two sides is equal to the less side and the difference between them ; but , by ...
Σελίδα 42
... fore AG and BH are also equal and pa- rallel ( Prop . 33 ) , and AGHB is a parallelo- gram ; but it is equal to the parallelogram ACDB , because it is on the same base AB and between the same parallels ( Prop . 35 ) ; and for a like rea ...
... fore AG and BH are also equal and pa- rallel ( Prop . 33 ) , and AGHB is a parallelo- gram ; but it is equal to the parallelogram ACDB , because it is on the same base AB and between the same parallels ( Prop . 35 ) ; and for a like rea ...
Σελίδα 46
... fore equal ( Prop . 43 ) ; but the parallelogram AD is equal to the given triangle G , therefore LA also is equal to G ; and it is applied to the given line AB : and also since ACD = △ ▽ ( Const . ) , and / ACD = / FAB = LAHL ( Prop ...
... fore equal ( Prop . 43 ) ; but the parallelogram AD is equal to the given triangle G , therefore LA also is equal to G ; and it is applied to the given line AB : and also since ACD = △ ▽ ( Const . ) , and / ACD = / FAB = LAHL ( Prop ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ACDB adjacent angles angles equal antecedent Axioms base bisected centre chord circumference coincide consequently Const definition demonstrated describe diagonal diameter difference divided draw equal angles equal Prop equal sides equiangular equilateral triangle equimultiples Euclid Euclid's Elements external angle extremities fore fourth fractional Geometry given angle given circle given line given point given straight line given triangle greater hypotenuse inscribed internal intersect isosceles triangle less line drawn lines be drawn magnitudes manner meeting multiple opposite angles parallel parallelogram perpendicular point of contact PROB produced proportional Proposition quadrilateral figure rectangle contained rectilinear figure remaining angles respectively equal right angle segment semiperimeter sides AC sides equal square of half subtending taken tangent THEOR third triangles ABC unequal vertex whole line
Δημοφιλή αποσπάσματα
Σελίδα 126 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 155 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 83 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Σελίδα 129 - ... figures are to one another in the duplicate ratio of their homologous sides.
Σελίδα 47 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 90 - BFE : (i. def. 10.) therefore, in the two triangles, EAF, EBF, there are two angles in the one equal to two angles in the other, each to each ; and the side EF, which is opposite to one of the equal angles in each, is common to both ; therefore the other sides are equal ; (i.
Σελίδα 117 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Σελίδα 56 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Σελίδα 60 - Iff 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.
Σελίδα 78 - Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the same side of the same straight line AB, not coinciding with one another.