The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 sider |
Inni boken
Resultat 1-5 av 19
Side 356
... proportionally . ( 2 ) Conversely : -If two sides of a triangle , or those sides produced , be cut proportionally , the straight line joining the points of section shall be parallel to the base . ( 1 ) Let the st . line DE , || to the ...
... proportionally . ( 2 ) Conversely : -If two sides of a triangle , or those sides produced , be cut proportionally , the straight line joining the points of section shall be parallel to the base . ( 1 ) Let the st . line DE , || to the ...
Side 368
... proportional . In As ABC , DEF , let △ A = ≤ D , and let AB BC :: DE : EF ; then if C and F are each acute , or each obtuse , or if either C or F is a right △ , B AABC is equiangr . to △ DEF . A H C да F FE From AB , AC , produced ...
... proportional . In As ABC , DEF , let △ A = ≤ D , and let AB BC :: DE : EF ; then if C and F are each acute , or each obtuse , or if either C or F is a right △ , B AABC is equiangr . to △ DEF . A H C да F FE From AB , AC , produced ...
Side 371
... proportional between CB , BD . Ex . 696. - BA is a tangent to a circle ADC , and BDC is a secant ; show that AB is a mean proportional between CB , BD . PROPOSITION 9. PROBLEM . From a given straight line to Book VI . Prop . 8 . 371.
... proportional between CB , BD . Ex . 696. - BA is a tangent to a circle ADC , and BDC is a secant ; show that AB is a mean proportional between CB , BD . PROPOSITION 9. PROBLEM . From a given straight line to Book VI . Prop . 8 . 371.
Side 374
... , such that AC : CB and AD : DB in the given ratio of AP : PB . Then use VI . 3 and VI . A. to show that angle CPD is a right angle ( see Ex . 16 ) . PROPOSITION 11. PROBLEM . To find a third proportional to 374 Euclid's Elements .
... , such that AC : CB and AD : DB in the given ratio of AP : PB . Then use VI . 3 and VI . A. to show that angle CPD is a right angle ( see Ex . 16 ) . PROPOSITION 11. PROBLEM . To find a third proportional to 374 Euclid's Elements .
Side 375
... proportional to two given straight lines . Let A , B be the two given st . lines ; it is reqd . to find a third propl . to them . D M A B From any pt . D draw two st . lines DHL , DGM not in the same st . line , and such that DH = A ...
... proportional to two given straight lines . Let A , B be the two given st . lines ; it is reqd . to find a third propl . to them . D M A B From any pt . D draw two st . lines DHL , DGM not in the same st . line , and such that DH = A ...
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The Harper Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Euclid,Edward Mann Langley,W. Seys Phillips Uten tilgangsbegrensning - 1890 |
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Euclid,Edward Mann Langley,W. Seys Phillips Uten tilgangsbegrensning - 1894 |
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
bisect bisector Brocard point chord circum-circle of triangle circumference coincide common concyclic congruent cyclic quadrilateral demonstration described diagonals diameter diamr divided draw equal angles equiangr equiangular equidistant equilateral triangle equimultiples Euclid exterior angle Geometry given circle given point given ratio given st given straight line given triangle greater Hence inscribed intersect isosceles isosceles triangle Join Let ABC locus magnitude meet mid-point opposite sides parallel parallelogram pass pentagon perpendicular plane produced Prop PROPOSITION PROPOSITION 13 radical axis radius rect rectangle contained reqd rhombus right angles segment Show sides BC similar Similarly Simson's line square straight line drawn student subtended symmedian symmedian point tangent THEOREM touch triangle ABC vertex vertices
Populære avsnitt
Side 21 - 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.
Side 369 - 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.
Side 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Side 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 370 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Side 96 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 40 - Any two sides of a triangle are together greater than the third side.
Side 143 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.
Side 407 - 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.
Side 156 - 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...