## The geometry of the three first books of Euclid, by direct proof from definitions alone, by H. Wedgwood |

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Side 83

If a straight line be divided into two equal

If a straight line be divided into two equal

**and also into two unequal parts , the rectangle contained by the unequal parts , together with the square of the line**between the points of section , is equal to the square of half the line .### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

analysis attained Author base Book centre Chap circle circumference cloth coincide common conception construction cutting definition diameter direction distance divided double drawn Edition elements English equal Euclid expressed fall figure fundamental geometry given greater Greek Illustrations Join known less lettered London magnitude meet motion moving necessary numerous object opposite originally parallel parallelogram passing perpendicular plane position possible Principles produced Professor proof Prop proportion proposition reason rectangle contained relation remaining respectively right angles School segment side space square square of BC straight line student surface third tion touch track transverse triangle triangle A B C twice the rectangle University College Vols Volume wherefore whole wholly

### Populære avsnitt

Side 62 - 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.

Side 64 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

Side 98 - Museum of Science and Art. THE MUSEUM OF SCIENCE AND ART. Edited by DIONYSIUS LARDNER, DCL, formerly Professor of Natural Philosophy and Astronomy in University College, London. With upwards of 1 200 Engravings on Wood.

Side 80 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 25 - 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 sides.

Side 78 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.

Side 97 - This is quite a novelty in chronological literature. It is an universal almanac — universal, that is, as respects time, past, present, and future. The main object of it is, as the compiler states, to supply the place of an old almanac, which is never at hand when wanted ; of the older almanac, which never was at hand ; and of the universal almanac in every shape IA more useful chronological handbook could scarcely be conceived.

Side 24 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.

Side 26 - If two triangles have two sides of the one equal to two sides of the...