Books Books
To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Elements of geometry, based on Euclid, books i-iii - Page 71
by Edward Atkins - 1876 - 119 pages

## The Architecture of Bridge Design

David Bennett - Bridges - 1997 - 212 pages
...beauty. It was neatly summarised by Euclid in two of his propositions: "to cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square m the remaining segment" and "to cut a given finite line in extreme...

## The Mathematics of Measurement: A Critical History

John J. Roche, ROCHE - Mathematics - 1998 - 364 pages
...Euclid book II, proposition 1 1 is an example of a construction problem: To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment'. Heath points out24 that this is equivalent,...

## De arte mensurandi

Johannes de Muris, Hubertus Lambertus Ludovicus Busard - History - 1998 - 398 pages
...radius of the circle (Campanus IV. 15 Porism). Prop. 3 reads as follows: To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment (Campanus 11.11). From Prop. 4: If the radius...

## Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 292 pages
...Hint: See Figure 5.6. Exercise 5.9: Proposition 1 1 in Book II states: To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment. Which type of quadratic equation can be solved...

## Greek Science of the Hellenistic Era: A Sourcebook

Georgia Lynette Irby-Massie, Paul T. Keyser, Paul Turquand Keyser - History - 2002 - 440 pages
...proportion used in the Parthenon, which we call (sqrt(5)+1)/2 = 1.618...] To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to die square on the remaining segment. Let AB be die given straight line (Figure...