## A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ... |

### From inside the book

Results 1-5 of 5

Page 115

And if AB be moved direarly forward , to EF , still keeping aarallel to its first

position , it will

Hence , it is plain that the Angles x , y and z , made with GE , are all equal to one

another ...

And if AB be moved direarly forward , to EF , still keeping aarallel to its first

position , it will

**also**coincide with EF , and the Angle GAB , or ACD , with CEF .Hence , it is plain that the Angles x , y and z , made with GE , are all equal to one

another ...

Page 222

Let L be the Center of the Circle ; draw AL , BL , & c .

DEM . AL , BL , & c . are perpendicular to FG , GH , & c . -83 and they are all equal

between themselves - - - Ax . 1.3 The Angle ALB is equal to BLC , by

Construction .

Let L be the Center of the Circle ; draw AL , BL , & c .

**also**draw FL , GL , & c .DEM . AL , BL , & c . are perpendicular to FG , GH , & c . -83 and they are all equal

between themselves - - - Ax . 1.3 The Angle ALB is equal to BLC , by

Construction .

Page 257

Axiom XI . In four proportional Quantities , i . e . when any one is to another , as a

third is Ato the fourth , ( Def . 6. ) whether the first be equal Bto , greater , or less

than the second , the third is a

Axiom XI . In four proportional Quantities , i . e . when any one is to another , as a

third is Ato the fourth , ( Def . 6. ) whether the first be equal Bto , greater , or less

than the second , the third is a

**also**equal to , greater , or less than the fourth . Page 269

1 none have given a Demonstration of Inverse Ratio ; which being proved , every

Converse Ratio is

and has very judiciously introduced it , as an additional Proposition ( B ; ) after ...

1 none have given a Demonstration of Inverse Ratio ; which being proved , every

Converse Ratio is

**also**proved . Professor Simson is aware of that deficiency ,and has very judiciously introduced it , as an additional Proposition ( B ; ) after ...

Page 290

And , the Lines which ' proceed from a Point will

parallel Lines . E Let AB and CD be parallel Lines . From any Point , E , at

pleasure , if the Right Lines EA , EF , & c . are drawn , F G B cuting the Parallels ,

in A ...

And , the Lines which ' proceed from a Point will

**also**be cut proportionally , by theparallel Lines . E Let AB and CD be parallel Lines . From any Point , E , at

pleasure , if the Right Lines EA , EF , & c . are drawn , F G B cuting the Parallels ,

in A ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... Thomas Malton No preview available - 2016 |

### Common terms and phrases

ABCD added alſo Altitudes analogous Area Baſe becauſe biſected Book called Center Chord Circle Circumference common Cone conf conſequently Conſtruction contained cuting Cylinder Demonſtration deſcribe Diagonal Diameter difference divided draw drawn equal Euclid evident extreme fame Feet Figure firſt formed four fourth given given Line greater half Hence Inches inſcribed join laſt leſs manner mean meaſure multiplied muſt oppoſite parallel Parallelogram Parallelopiped Pentagon perpendicular Plane Point Poligon Priſm Prob PROBLEM produced Proportion Propoſition proved Pyramid Quantities Radius Ratio Rect Rectangle reſpectively Right Angles Right Line ſame ſame Ratio ſay ſeeing Segment Sides ſimilar Solid ſome Sphere Square ſuch Surface taken Terms THEOREM third thoſe touch Triangle uſe wherefore whole whoſe

### Popular passages

Page 124 - When you have proved that the three angles of every triangle are equal to two right angles...

Page 221 - 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.

Page 285 - EG, let fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter DS, EF (p.

Page 284 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Page 186 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two; and when the adjacent angles are equal, they are right angles.

Page 248 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 161 - In any triangle, if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base.

Page 160 - In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base.

Page 250 - Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F.

Page 124 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.