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

### Dentro del libro

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Página 30

Acute and obtuse angled triangles are in general called oblique angled triangles

, in all which may be called the base ... The perpendicular height of a triangle is a

line drawn from the vertex to the base perpendicularly : thus if the

Acute and obtuse angled triangles are in general called oblique angled triangles

, in all which may be called the base ... The perpendicular height of a triangle is a

line drawn from the vertex to the base perpendicularly : thus if the

**triangle ABC**... Página 38

If in any two

severally equal to DE , DF in the other , and ... If the

be laid on the triangle DEF , so as to make the points A and B coincide with D

and E ...

If in any two

**triangles**,**ABC**, DEF , there be two sides , AB , AC in the one ,severally equal to DE , DF in the other , and ... If the

**triangle ABC**be supposed tobe laid on the triangle DEF , so as to make the points A and B coincide with D

and E ...

Página 44

Hence it is plain that triangles on the same or equal bases , and between the

same parallels , are equal , seeing ( by cor 2. theo . 12. ) they are the halves of

their respective parallelogram . THEOREM XIV . In every right - angled

Hence it is plain that triangles on the same or equal bases , and between the

same parallels , are equal , seeing ( by cor 2. theo . 12. ) they are the halves of

their respective parallelogram . THEOREM XIV . In every right - angled

**triangle**,**ABC**... Página 102

EFORE we proceed to the solution of the four cases of Oblique angular triangles ,

it is necessary to premise the following theorems . THEOREM I. Plate V. In any

plane

EFORE we proceed to the solution of the four cases of Oblique angular triangles ,

it is necessary to premise the following theorems . THEOREM I. Plate V. In any

plane

**triangle ABC**, the sides are proportional to the sines of their opposite ... Página 133

And in the

113 36 ° 30 ' 175. 6 . In the triangle DBC , you have DBC = ABCABD = 72 ° ;

likewise the sides BD , BC , as before found , given to find DC . 3. BD + BC : BD -

BC ...

And in the

**triangle ABC**, find BC thus , 2. S. ACB : AB :: S. CAB : BC . 22 ° 30 '113 36 ° 30 ' 175. 6 . In the triangle DBC , you have DBC = ABCABD = 72 ° ;

likewise the sides BD , BC , as before found , given to find DC . 3. BD + BC : BD -

BC ...

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### 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.