Ever wonder what comes after primary, secondary, or tertiary in counting sequences? These terms come from Latin numerals which are expressed in Cardinal, Ordinal, and several other forms. These terms are used to describe the rank order in which an element exists relative to other elements.

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For example—the Latin Ordinal *primus, *meaning first, gives us *primary* is used to describe the first-order rank of an element. Primary elections, primary contact, primary residence—these all indicate the first of something where there may be others.

## Naming the Numerals

These terms are used in variation throughout the fields of Science, Engineering, and Mathematics as ways to count and signify order as well as sometimes to simply assign arbitrary taxonomic value. Below is a collection of the first 10 Latin numerals though they continue far beyond.

## Primary

**Ordinal**: *Primus*

**Cardinal**: *Unus*

The first element of a counting sequence and also used to indicate the principle matter of importance. Examples include primary elections, primary schools, and primary contact numbers. The word Primary finds its root from the Latin words *primus* and *arius *used to indicate a primary rank in military contexts or, similar to its modern use, the principal matter of concern.

## Secondary

**Ordinal**: *Secundus*

**Cardinal**: *Duo*

Secondary describes the term directly preceding the primary term or element in a counting sequence or the primary matter of concern. Examples of secondary include secondary elections, secondary schools, or a secondary coil in certain electrical circuits. The word *secondary* comes from the Middle English *secundarie* which is descended from the Latin word *secundus *that means “to follow” and can be compared with the term *sequor* which bears the same meaning.

## Tertiary

**Ordinal**: *Tertius *

**Cardinal**: *Tres*

Tertiary is used to describe the third level within a sequence of elements, events, or otherwise meaningful distinctions. Example In Geology, Tertiary refers to the first period of the Cenezoic era. Tertiary comes from the Latin word *tertius* which means third. Examples include tertiary compounds in chemistry describing those that have been subjected to the substitution of 3 atoms.

## Quaternary

**Ordinal: ***Quartus*

**Cardinal**: *Quattuor*

Quaternary is used to describe an element as being of fourth-order rank in a sequence or collection. In Geology, the term quaternary is used to describe the most recent period in the Cenozoic era, directly proceeding the Tertiary Period. Quaternary comes from the Latin *quarternarius* meaning “to contain or be made of four,” which is a combination of the words *quaterni* and *arius*. In chemistry, the term quaternary describes certain types of compounds including amines and ammonium salts.

## Quinary

**Ordinal: ***Qunitas*

**Cardinal**: *Quinque*

Quinary is used to describe an element of fifth-order rank or, more generally, to describe something made of five sub-units. The term *quinary* comes from the Latin word quinarius meaning “containing five each” which represents a combination of the terms *quinus *and *arius*. In Zoology, quinary refers to an outdated system of classification by which the Animal kingdom was divided into 5 subkingdoms and each subkingdom was divided into five subclasses. Quinary also refers to a numeral system that uses 5 as the base value—possibly having come about in connection to there being five fingers on the human hand.

## Senary

**Ordinal:** *Sextus*

**Cardinal**: *Sex*

Senary is used to describe an element of six-order rank within a larger sequence or collection. It comes from the Latin term *senarius* meaning “consisting of six each” which is a combination of the words *seni* and *arius*. In mathematics, a senary numeral system is also known as a base-6 or heximal number system. It is thought the senary numeral systems evolved from the use of five fingers and the closed fist to represent terms 0-5 (six total terms.)

## Septenary

**Ordinal:** *Septimus*

**Cardinal**: *Septum*

Septenary is used to describe an element of seventh-order rank within a sequence or collection of elements. It comes from the Latin term *septenarius* meaning “consisting of seven each” and is made of the terms *septeni* and *arius. *Septenary is used in Theosophy to describe the seven principles of man, and also describes the system of counting 7-day weeks in some contexts.

## Octonary

**Ordinal:** *Octavus*

**Cardinal**: *Octo*

Octonary is used to describe an element of seventh-order rank within a sequence or collection of elements. It comes from the Latin term *octonarius* meaning “containing eight” which is made of the terms *octoni* and *arius*. Octonary can be used to refer to the style of poetry using 8-lines. While similar in concept, Octonary is not used to describe octal counting systems—a means of numerical representation in computer science.

## Nonary

**Ordinal: ***Nonus*

**Cardinal**: *Novem*

Nonary is used to describe an element of ninth-order rank within a collection or sequence of elements. It comes from the Latin term *nonarius* meaning “containing nine” which is a combination of the terms *nonus* and *arius*. Nonary is used to describe less common base 9 counting systems where the digits 10 represent the value 9. In decimals, a nonary counting system uses only digits 0-8 similar in concept to how binary systems use the values 0-1.

## Denary

**Ordinal: ***Decimus*

**Cardinal**: *Decem*

Denary is used to describe an element of tenth-order rank within a system, collection, or sequence of elements. It comes from the Middle English term *denarie* which evolved from the Latin term *denarius* meaning “containing ten” which was sometimes used as *denarius nummus* to describe a coin of ten subunits. Denary is often used to describe the decimal counting system which uses a base of 10.

## Beyond Ten

The numeral system presented here is the Latin version (*latinate*) of the English Ordinal Counting system. There are a great many more in this sequence but, other than a few terms such as hexadecimal, the terms become increasingly rare in their usage. For a full listing of these terms just check out the Wikipedia entry for numerical systems which includes a more exhaustive listing—albeit with a sparser presentation of definition.