A Text-book of Euclid's Elements for the Use of Schools, Libro 1Macmillan, 1904 - 456 páginas |
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Página 307
... proportional to A , B , and C. Definition 6. Two terms in a proportion are said to be homo- logous when they are both antecedents , or both consequents of the ratios . Definition 7. The ratio of one magnitude to another is greater than ...
... proportional to A , B , and C. Definition 6. Two terms in a proportion are said to be homo- logous when they are both antecedents , or both consequents of the ratios . Definition 7. The ratio of one magnitude to another is greater than ...
Página 308
... proportional to A and C , and C is called a third proportional to A and B. Definition 10. Three or more magnitudes are said to be in continued proportion when the ratio of the first to the second is equal to that of the second to the ...
... proportional to A and C , and C is called a third proportional to A and B. Definition 10. Three or more magnitudes are said to be in continued proportion when the ratio of the first to the second is equal to that of the second to the ...
Página 316
... proportional to A and B , and Y a third pro- portional to C and D , so that A B :: B : X , and C : D :: D : Y ; then because A : B :: C : D , .. , ex æquali , . B : X :: D : Y ; AX : C : Y. A B and C : D , But A : X and C : Y are ...
... proportional to A and B , and Y a third pro- portional to C and D , so that A B :: B : X , and C : D :: D : Y ; then because A : B :: C : D , .. , ex æquali , . B : X :: D : Y ; AX : C : Y. A B and C : D , But A : X and C : Y are ...
Página 321
... proportional to a and c ; and c is called a third proportional to a and b . When four magnitudes are in proportion , namely when a : b :: c : d , then d is called a fourth proportional to a , b , and c . Definition 10. A series of ...
... proportional to a and c ; and c is called a third proportional to a and b . When four magnitudes are in proportion , namely when a : b :: c : d , then d is called a fourth proportional to a , b , and c . Definition 10. A series of ...
Página 325
... proportional when a side of the first figure is to a side of the second as the remaining side of the second figure is to the remaining side of the first . 5. A straight line is said to be divided in extreme and mean ratio when the whole ...
... proportional when a side of the first figure is to a side of the second as the remaining side of the second figure is to the remaining side of the first . 5. A straight line is said to be divided in extreme and mean ratio when the whole ...
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Términos y frases comunes
ABCD AC is equal adjacent angles Algebra angle BAC angle equal base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equiangular Euclid Euclid's exterior angle find the locus given circle given point given straight line given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn plane XY polygon produced Proof proportional PROPOSITION PROPOSITION 13 prove quadrilateral radical axis radius rectangle contained rectilineal figure regular polygon right angles segment shew shewn side BC Similarly square straight line drawn tangent THEOREM triangle ABC twice the rect vertex vertical angle
Pasajes populares
Página 353 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Página 340 - 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.
Página 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Página 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Página 162 - 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...
Página 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Página 18 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Página 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.