Euclid's Elements of plane geometry [book 1-6] with explanatory appendix, and supplementary propositions, by W.D. Cooley1840 |
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Seite 20
... PARALLELOGRAM is that of which the opposite sides are parallel . 27. Of parallelograms , that is a SQUARE which has all its sides and angles equal . 28. An OBLONG is that which has equal angles , but not equal sides . 29. A RHOMB is ...
... PARALLELOGRAM is that of which the opposite sides are parallel . 27. Of parallelograms , that is a SQUARE which has all its sides and angles equal . 28. An OBLONG is that which has equal angles , but not equal sides . 29. A RHOMB is ...
Seite 41
... parallelogram ( ACDB ) are equal , and it is bisected or divided into two equal parts by a diagonal ( AD ) . C A B C = / B ; and Since AB is parallel to CD , and AC to BD , the triangles ACD , DBA have △ ADC = / DAB , and △ CAD ...
... parallelogram ( ACDB ) are equal , and it is bisected or divided into two equal parts by a diagonal ( AD ) . C A B C = / B ; and Since AB is parallel to CD , and AC to BD , the triangles ACD , DBA have △ ADC = / DAB , and △ CAD ...
Seite 42
... parallelogram be a diagonal of the other , then it is evident that the paral- c lelograms are , each of them ... parallelogram ACDB , because it is on the same base AB and between the same parallels ( Prop . 35 ) ; and for a like rea ...
... parallelogram be a diagonal of the other , then it is evident that the paral- c lelograms are , each of them ... parallelogram ACDB , because it is on the same base AB and between the same parallels ( Prop . 35 ) ; and for a like rea ...
Seite 44
... parallelogram ( ACDB ) and a triangle ( AFB ) are upon the same base ( AB ) and between the same parallels ( AB , CF ) , the parallelogram is double of the triangle . = Draw the diagonal CB ; and then the triangle c ACB AFB ( Prop . 37 ) ...
... parallelogram ( ACDB ) and a triangle ( AFB ) are upon the same base ( AB ) and between the same parallels ( AB , CF ) , the parallelogram is double of the triangle . = Draw the diagonal CB ; and then the triangle c ACB AFB ( Prop . 37 ) ...
Seite 45
... parallelogram are equal . Since AD is the diagonal of the parallelogram ACDB , the triangle ACD = ABD ( Prop . 34 ) ; and in like manner the parallelograms AEKH , KGDF about the diagonal are bisected by the diagonal , and the triangles ...
... parallelogram are equal . Since AD is the diagonal of the parallelogram ACDB , the triangle ACD = ABD ( Prop . 34 ) ; and in like manner the parallelograms AEKH , KGDF about the diagonal are bisected by the diagonal , and the triangles ...
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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'.
Seite 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.
Seite 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.
Seite 129 - ... figures are to one another in the duplicate ratio of their homologous sides.
Seite 47 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.