## A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ... |

### Dentro del libro

Resultados 1-5 de 5

Página 39

drawn right lines to the extremities of the given one , they with it will form an

isosceles triangle . THEOREM VII . The angle BCD at the centre of a circle ABED

, is ...

**Hence**if from any point in a perpendicular which bisects a given line , there bedrawn right lines to the extremities of the given one , they with it will form an

isosceles triangle . THEOREM VII . The angle BCD at the centre of a circle ABED

, is ...

Página 40

thus ADB is measured by half the arc AB , but as the arc AB is less than a

semicircle , therefore half the arc AB , or the angle ADB is less than half a

semicircle ...

**Hence**an angle in a segment greater than a semicircle is less than a right angle ;thus ADB is measured by half the arc AB , but as the arc AB is less than a

semicircle , therefore half the arc AB , or the angle ADB is less than half a

semicircle ...

Página 41

a line drawn from the centre perpendicular to a chord , bisects thạt chord at right

angles ; therefore , conversely , a line bisecting a chord at right angles must ...

**Hence**it follows , that any line bisecting a chord at right angles , is a diameter ; fora line drawn from the centre perpendicular to a chord , bisects thạt chord at right

angles ; therefore , conversely , a line bisecting a chord at right angles must ...

Página 43

bisects the same , inasmuch as the triangle ABD = BCD , as now proved . Cor . 2.

**Hence**the quadrilateral figure ABCD is a parallelogram , and the diagonal BDbisects the same , inasmuch as the triangle ABD = BCD , as now proved . Cor . 2.

**Hence**also the triangle ABD on the same base , AB , and between the same ... Página 49

I.

AE . Cor . 2. It also appears that a right line , which divides two sides of a triangle

proportionally , must be parallel to the remaining side . Cor . 3.

I.

**Hence**also AC : AB :: AD : AE : For AC : AB :: ( AEC : AEB :: ABD : AEB ) :: AD :AE . Cor . 2. It also appears that a right line , which divides two sides of a triangle

proportionally , must be parallel to the remaining side . Cor . 3.

**Hence**also theo .### Comentarios de la gente - Escribir un comentario

No encontramos ningún comentario en los lugares habituales.

### Términos y frases comunes

acres angle Answer base bearing called centre chains chord circle Co-sec Co-sine Co-tang column contained decimal difference direct distance divided division draw drawn east edge equal EXAMPLE feet field field-book figures four four-pole fourth give given greater ground half height Hence inches laid land Lat Dep length less logarithm manner measure method multiplied needle object observe opposite parallel perches perpendicular plain plane Plate pole prob PROBLEM proportion quantity quotient radius reduce remainder right angles right line root scale Secant sect side sights sine square station suppose survey taken Tang tangent theo THEOREM third triangle triangle ABC true turn variation whence whole

### Pasajes populares

Página 25 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.

Página 207 - ... that triangles on the same base and between the same parallels are equal...

Página 40 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Página 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.

Página 103 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.

Página 31 - Figures which consist of more than four sides are called polygons ; if the sides are all equal to each other, they are called regular polygons. They sometimes are named from the number of. their sides, as a five-sided figure is called a pentagon, one of six sides a hexagon, &"c.

Página 31 - ... they are called regular polygons. They sometimes are named from the number of their sides, as a five-sided figure is called a pentagon, one of. six sides a hexagon, &c. but if their sides are not equal to each other, then they are called irregular polygons, as an irregular pentagon, hexagon, &c.

Página 45 - The hypothenuse of a right-angled triangle may be found by having the other two sides ; thus, the square root of the sum of the squares of the base and perpendicular, will be the hypothenuse. Cor. 2. Having the hypothenuse and one side given to find the other; the square root of the difference of the squares of the hypothenuse and given side will be the required side.

Página 265 - As the length of the whole line, Is to 57.3 Degrees,* So is the said distance, To the difference of Variation required. EXAMPLE. Suppose it be required to run a line which some years ago bore N. 45°.

Página 32 - Things that are equal to one and the same thing are equal to one another." " If equals be added to equals, the wholes are equal." " If equals be taken from equals, the remainders are equal.