## Geometry, Old and New, Its Problems and Principles: A Paper |

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

Geometry, Old and New, Its Problems and Principles: A Paper Benjamin Gratz Brown Ingen forhåndsvisning tilgjengelig - 2009 |

### Vanlige uttrykk og setninger

applied arcs arithmetical assume base beauty becomes bounded called century circle circumference close combinations conception condition construction contained course curve definite demonstration describe designation determination diagram diameter direction distinction divided drawn elements entirely equal equation establishes exist expression extension extremity fact figures fixed former four geometry give given greater half human idea illustration important indicated infinite inscribed interest intersection known less likewise limit magnitudes mathematics matter means measure method mind multiple numbers obtained opposite origin parallel parallelogram perhaps perpendicular Persian plane position present problems properties proportion propositions pure radius ratio reasoning reference regard relations remains represent result right angles right triangle schools seen segment shown sides similar simple solution space square straight line studies surface taken thing thought tion triangle true truth unit volume whilst whole wonder

### Populære avsnitt

Side 14 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.

Side 19 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Side 10 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

Side 17 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef.

Side 23 - ... distance between the centres of the inscribed circle and of the circle through the middle points of sides has been proved to be exactly the difference between their radii ; and the same argument applies to any of the four circles which touch the three sides of the given triangle ; hence (5) The circle which passes through the middle points of the sides of a triangle touches the four circles which touch the three sides. This theorem was new both to Dr Hart and myself,* but I have lately learned...

Side 8 - THEOREM. 35. Of two oblique lines drawn from the same point to the same straight line, that is the greater which cuts off upon the line the greater distance from the perpendicular. Let PC be the perpendicular from P to AB, and suppose CE > CD; thenPU> PD. For, produce PC to P', making CP

Side 15 - Two triangles are similar if an angle of one equals an angle of the other and the sides including these angles are proportional.

Side 18 - Two diagonals of a regular pentagon, not drawn from a common vertex, divide each other in extreme and mean ratio.

Side 31 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.

Side 16 - In any triangle, if a straight line is drawn from the vertex to the middle of the base, the sum of the squares of the other two sides is equivalent to twice the square of the bisecting line, together with twice the square of half the base.