## Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green |

### Inni boken

Resultat 1-5 av 5

Side 44

... and in other branches of

enables the Surveyor to ascertain the distance of an inaccessible object , by the

method of Representative Values or of Construction : thus , there are three

objects ...

... and in other branches of

**practical**Mathematics . 2 . The use of parallel linesenables the Surveyor to ascertain the distance of an inaccessible object , by the

method of Representative Values or of Construction : thus , there are three

objects ...

Side 51

By the last two propositions we arrive at a

space , as ABC , into two equal parts ; for if the base BC be bisected from the

vertex A by AK , then , because the two triangles ABK and ACK are on equal

bases BK ...

By the last two propositions we arrive at a

**practical**way of dividing a triangularspace , as ABC , into two equal parts ; for if the base BC be bisected from the

vertex A by AK , then , because the two triangles ABK and ACK are on equal

bases BK ...

Side 61

A

proportion of 3 , 4 , and 5 , and constructing with them a rt . angled triangle BAC ;

on each of the three sides draw a square , and sub - divide each square ; that on

AC ...

A

**practical**illustration of Prop . 47 , may be given by taking three lines in theproportion of 3 , 4 , and 5 , and constructing with them a rt . angled triangle BAC ;

on each of the three sides draw a square , and sub - divide each square ; that on

AC ...

Side 62

2 The height of any elevation on the earth ' s surface is so small when compared

with the earth ' s diameter , that for

ascertaining the height of mountains , we may consider the earth ' s actual

diameter ...

2 The height of any elevation on the earth ' s surface is so small when compared

with the earth ' s diameter , that for

**practical**purposes , as levelling , andascertaining the height of mountains , we may consider the earth ' s actual

diameter ...

Side 64

CRITICAL NOTICES , “ This is a most valuable edition of Euclid , and for the

purposes of the

have met with no edition of Euclid ( in a considerable experience ) so likely to aid

...

CRITICAL NOTICES , “ This is a most valuable edition of Euclid , and for the

purposes of the

**practical**tutor will be found a very great aid . ” “ On the whole , wehave met with no edition of Euclid ( in a considerable experience ) so likely to aid

...

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### Vanlige uttrykk og setninger

ABCD added angle equal apply ascertain assumed Axioms base base BC bisected centre circle circumference coincide common Conc construct contained definition demonstration describe diagonal diameter distance divided draw drawn earth's equal Euclid extremity fall feet figure four Geometry given given point greater half height impossible inches inference intersect join length less line BC measure meet miles named object opposite parallel parallelogram perpendicular plane practical principle produced Prop proposition proved reason rectangle rectil rectilineal representative right angles scale sides square straight line suppose surface thing third triangle true truth units Wherefore whole

### Populære avsnitt

Side 36 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Side 17 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 17 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.

Side 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.

Side 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Side 16 - LET it be granted that a straight line may be drawn from any one point to any other point.

Side 54 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 21 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.

Side 22 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity.

Side 12 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.